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The mean and variance, respectively, of a binomial distribution for $n$ independent trails with the probability of success as $p$, are $\sqrt{np},np\left ( 1-2p \right )$ $\sqrt{np},\sqrt{np\left ( 1-p \right )}$ $np,np$ $np, np\left ( 1-p \right )$
asked Mar 1 in Probability and Statistics jothee 4.9k points
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A $\text{PERT}$ network has $9$ activities on its critical path. The standard deviation of each activity on the critical path is $3$. The standard deviation of the critical path is $3$ $9$ $27$ $81$
asked Mar 1 in Probability and Statistics jothee 4.9k points
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Consider a binomial random variable $\text{X}$. If $X_{1},X_{2},\dots ,X_{n}$ are independent and identically distributed samples from the distribution of $\text{X}$ with sum $Y=\sum_{i=1}^{n}X_{i}$, then the distribution of $\text{Y}$ as $n\rightarrow \infty$ can be approximated as Exponential Bernoulli Binomial Normal
asked Feb 22 in Probability and Statistics gatecse 1.6k points
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Customers arrive at a shop according to the Poisson distribution with a mean of $10$ customers/hour. The manager notes that no customer arrives tor the first $3$ minutes after the shop opens. The probability that a customer arrives within the next $3$ minutes is $0.39$ $0.86$ $0.50$ $0.61$
asked Feb 22 in Probability and Statistics gatecse 1.6k points
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The sum of two normally distributed random variables $X$ and $Y$ is always normally distributed normally distributed, only if $X$ and $Y$ are independent normally distributed, only if $X$ and $Y$ have the same standard deviation normally distributed, only if $X$ and $Y$ have the same mean
asked Sep 18, 2020 in Probability and Statistics jothee 4.9k points
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A fair coin is tossed $20$ times. The probability that ‘head’ will appear exactly $4$ times in the first ten tosses, and ‘tail’ will appear exactly $4$ times in the next ten tosses is _________ (round off to $3$ decimal places)
asked Sep 18, 2020 in Probability and Statistics jothee 4.9k points
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The probability that a part manufactured by a company will be defective is $0.05$. If $15$ such parts are selected randomly and inspected, then the probability that at least two parts will be defective is _____ (round off to two decimal places).
asked Feb 9, 2019 in Probability and Statistics Arjun 24.6k points
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The variable $x$ takes a value between $0$ and $10$ with uniform probability distribution. The variable $y$ takes a value between $0$ and $20$ with uniform probability distribution. The probability of the sum of variables $(x+y)$ being greater then $20$ is $0$ $0.25$ $0.33$ $0.50$
asked Feb 9, 2019 in Probability and Statistics Arjun 24.6k points
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A box contains $4$ red balls and $6$ black balls. Three balls are selected randomly from the box one after another, without replacement. The probability that the selected set contains one red ball and two black balls is $1/20$ $1/12$ $3/10$ $1/2$
asked Mar 20, 2018 in Probability and Statistics Andrijana3306 1.5k points
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Let $X_1$ and $X_2$ be two independent exponentially distributed random variables with means $0.5$ and $0.25$, respectively. Then $Y=\text{min}(X_1, X_2)$ is exponentially distributed with mean $1/6$ exponentially distributed with mean $2$ normally distributed with mean $3/4$ normally distributed with mean $1/6$
asked Feb 17, 2018 in Probability and Statistics Arjun 24.6k points
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The arrival of customers over fixed time intervals in a bank follow a Poisson distribution with an average of $30$ customers/hour. The probability that the time between successive customer arrival is between $1$ and $3$ minutes is _____ (correct to two decimal places)
asked Feb 17, 2018 in Probability and Statistics Arjun 24.6k points
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Let $X_1, \: X_2$ be two independent normal random variables with means $\mu_1, \: \ \mu_2$ and standard deviations $\sigma_1, \: \sigma_2$, respectively. Consider $Y=X_1-X_2; \: \mu_1 = \mu_2 =1, \: \sigma_1=1, \: \sigma_2=2$. Then, $Y$ is normally distributed ... $Y$ has mean $0$ and variance $5$, but is NOT normally distributed $Y$ has mean $0$ and variance $1$, but is NOT normally distributed
asked Feb 17, 2018 in Probability and Statistics Arjun 24.6k points
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A six-faced fair dice is rolled five times. The probability (in $\%$) of obtaining "ONE" at least four times is $33.3$ $3.33$ $0.33$ $0.0033$
asked Feb 17, 2018 in Probability and Statistics Arjun 24.6k points
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Four red balls, four green balls and four blue balls are put in a box. Three balls are pulled out of the box at random one after another without replacement. The probability that all the three balls are red is $1/72$ $1/55$ $1/36$ $1/27$
asked Feb 17, 2018 in Probability and Statistics Arjun 24.6k points
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The standard deviation of linear dimensions $P$ and $Q$ are $3 \mu$ m and $4 \mu$ m, respectively. When assembled, the standard deviation (in $\mu$ m) of the resulting linear dimension $(P+Q)$ is _________.
asked Feb 27, 2017 in Probability and Statistics Arjun 24.6k points
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A sample of $15$ data is as follows: $17, 18, 17, 17, 13, 18, 5, 5, 6, 7, 8, 9, 20, 17, 3$. The mode of the data is $4$ $13$ $17$ $20$
asked Feb 27, 2017 in Probability and Statistics Arjun 24.6k points
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Two coins are tossed simultaneously. The probability (upto two decimal points accuracy) of getting at least one head is _______.
asked Feb 27, 2017 in Probability and Statistics Arjun 24.6k points
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Three cards were drawn from a pack of $52$ cards. The probability that they are a king, a queen, and a jack is $\dfrac{16}{5525} \\$ $\dfrac{64}{2197} \\$ $\dfrac{3}{13} \\$ $\dfrac{8}{16575}$
asked Feb 24, 2017 in Probability and Statistics Arjun 24.6k points
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The area (in percentage) under standard normal distribution curve of random variable Z within limits from −$3$ to +$3$ is __________
asked Feb 24, 2017 in Probability and Statistics Arjun 24.6k points
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The probability that a screw manufactured by a company is defective is $0.1$. The company sells screws in packets containing $5$ screws and gives a guarantee of replacement if one or more screws in the packet are found to be defective. The probability that a packet would have to be replaced is _________
asked Feb 24, 2017 in Probability and Statistics Arjun 24.6k points
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Consider a Poisson distribution for the tossing of a biased coin. The mean for this distribution is $μ$. The standard deviation for this distribution is given by $\sqrt{\mu }$ $\mu ^2$ $\mu$ $1/\mu$
asked Feb 24, 2017 in Probability and Statistics Arjun 24.6k points
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If $P(X) = \displaystyle{\frac{1}{4}}$, $P(Y) = \displaystyle{\frac{1}{3}}$, and $P(X \cap Y) = \displaystyle{\frac{1}{12}}$, the value of $P(Y/X)$ is $\displaystyle{\frac{1}{4}} \\$ $\displaystyle{\frac{4}{25}} \\$ $\displaystyle{\frac{1}{3}} \\$ $\displaystyle{\frac{29}{50}}$
asked Feb 24, 2017 in Probability and Statistics Arjun 24.6k points
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The chance of a student passing an exam is $20 \%$. The chance of a student passing the exam and getting above $90 \%$ marks in it is $5 \%$. GIVEN that a student passes the examination, the probability that the student gets above $90 \%$ marks is $\dfrac{1}{18} \\ $ $\dfrac{1}{4} \\$ $\dfrac{2}{9} \\$ $\dfrac{5}{18}$
asked Feb 24, 2017 in Probability and Statistics Arjun 24.6k points
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The probability of obtaining at least two “SIX” in throwing a fair dice $4$ times is $425/432$ $19/144$ $13/144$ $125/432$
asked Feb 24, 2017 in Probability and Statistics Arjun 24.6k points
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Among the four normal distributions with probability density functions as shown below, which one has the lowest variance? $I$ $II$ $III$ $IV$
asked Feb 24, 2017 in Probability and Statistics Arjun 24.6k points
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The number of accidents occurring in a plant in a month follows Poisson distribution with mean as $5.2$. The probability of occurrence of less than $2$ accidents in the plant during a randomly selected month is $0.029$ $0.034$ $0.039$ $0.044$
asked Feb 19, 2017 in Probability and Statistics Arjun 24.6k points
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A group consists of equal number of men and women. Of this group $20$% of the men and $50$% of the women are unemployed. If a person is selected at random from this group, the probability of the selected person being employed is _______
asked Feb 19, 2017 in Probability and Statistics Arjun 24.6k points
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Consider an unbiased cubic dice with opposite faces coloured identically and each face coloured red, blue or green such that each colour appears only two times on the dice. If the dice is thrown thrice, the probability of obtaining red colour on top face of the dice at least twice is _______
asked Feb 19, 2017 in Probability and Statistics Arjun 24.6k points
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A box contains $25$ parts of which $10$ are defective. Two parts are being drawn simultaneously in a random manner from the box. The probability of both the parts being good is $\dfrac{7}{20} \\$ $\dfrac{42}{125} \\$ $\dfrac{25}{29} \\$ $\dfrac{5}{9}$
asked Feb 19, 2017 in Probability and Statistics Arjun 24.6k points
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Jobs arrive at a facility at an average rate of $5$ in an $8$ hour shift. The arrival of the jobs follows Poisson distribution. The average service time of a job on the facility is $40$ minutes. The service time follows exponential distribution. Idle time (in hours) at the facility per shift will be $\dfrac{5}{7} \\$ $\dfrac{14}{3} \\$ $\dfrac{7}{5} \\$ $\dfrac{10}{3}$
asked Feb 19, 2017 in Probability and Statistics Arjun 24.6k points
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In the following table, $x$ is a discrete random variable and $p(x)$ is the probability density. The standard deviation of $x$ is $\begin{array}{|c|c|c|c|} \hline x & 1 & 2 & 3 \\ \hline p(x) & 0.3 & 0.6 & 0.1 \\ \hline \end{array}$ $0.18$ $0.36$ $0.54$ $0.60$
asked Feb 19, 2017 in Probability and Statistics Arjun 24.6k points
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The jobs arrive at a facility, for service, in a random manner. The probability distribution of number of arrivals of jobs in a fixed time interval is Normal Poisson Erlang Beta
asked Feb 19, 2017 in Probability and Statistics Arjun 24.6k points
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The probability that a student knows the correct answer to a multiple choice question is $\dfrac{2}{3}$ . If the student does not know the answer, then the student guesses the answer. The probability of the guessed answer being correct is $\dfrac{1}{4}$. Given that the student has answered the question ... the correct answer is $\dfrac{2}{3} \\$ $\dfrac{3}{4} \\$ $\dfrac{5}{6} \\$ $\dfrac{8}{9}$
asked Feb 19, 2017 in Probability and Statistics piyag476 1.4k points
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Let $X$ be a normal random variable with mean $1$ and variance $4$. The probability $P \left \{ X \right.<\left. 0 \right \}$ is $0.5$ greater than zero and less than $0.5$ greater than $0.5$ and less than $1.0$ $1.0$
asked Feb 19, 2017 in Probability and Statistics piyag476 1.4k points
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