A random variable X has binomial distribution with n = 25 and p = 0.8 then standard deviation of X is

On a multiple-choice exam with 3 possible destructives for each of the 5 questions, the probability that a student will get 4 or more correct answers just by guessing is

If P(X = 0) = 1 − P(X = 1). If E(X) = 3Var(X), then P(X = 0).

If X is a binomial random variable with expected value 6 and variance 2.4, then P(X = 5) is 

The random variable X has the probability density function 
\(f(x)=\left\{\begin{array}{lr} a x+b & 0<x<1 \\ 0 & \text { otherwise } \end{array}\right.\) and \(E(X)=\frac { 7 }{ 12 } \), then a and b are respectively

Suppose that X takes on one of the values 0, 1, and 2. If for some constant k, \(P(X=i)=k P(X=i-1) \text { for } i=1,2 \text { and } P(X=0)=\frac{1}{7}\) , then the value of k is

Let X have a Bernoulli distribution with mean 0.4, then the variance of (2X - 3) is

If in 6 trials, X is a binomial variable which follows the relation 9P(X = 4) = P(X = 2), then the probability of success is

If \(f(x)=\frac { 1 }{ 2 } \) ,\(E\left( { x }^{ 2 } \right) =\frac { 1 }{ 4 } \) then var(x) is _____________

In a binomial distribution, if the mean is 8 and the variance is 6, then the number of trials is _____________

A die is tossed 5 times. Getting an odd number is considered a success. Then the variance of distribution of number of success is _____________

Var (2x ± 5) is =________

If the mean and variance of a binomial variate are 2 and 1 respectively, the probability that X takes a value greater than one is equal to__________.

A die is thrown 10 times. Getting a number greater than 3 is considered a success. The S.D of the number of successes is _________

For a Bernouli distribution

Three fair coins are tossed simultaneously. Find the probability mass function for number of heads occurred.

If the probability that a fluorescent light has a useful life of at least 600 hours is 0.9, find the probabilities that among 12 such lights
(i) exactly 10 will have a useful life of at least 600 hours;
(ii) at least 11 will have a useful life of at I least 600 hours;  
(iii) at least 2 will not have a useful life of at : least 600 hours.

Compute P(X = k) for the binomial distribution, B(n, p) where
n = 9, \(p=\frac { 1 }{ 2 } \), k = 7

Find the binomial distribution function for each of the following.
(i) Five fair coins are tossed once and X denotes the number of heads.
(ii) A fair die is rolled 10 times and X denotes the number of times 4 appeared.

In a pack of 52 playing cards, two cards are drawn at random simultaneously. If the number of black cards drawn is a random variable, find the values of the random variable and number of points in its inverse images.

A six sided die is marked '2' on one face, '3' on two ofits faces, and '4' on remaining three faces. The die is thrown twice. If X denotes the total score in two throws, find the values of the random variable and number of points in its inverse images.

For the random variable X with the given probability mass function as below, find the mean and variance \(f(x)= \begin{cases}2(x-1) & 1

The probability that a certain kind of component will survive a electrical test is \(\frac { 3 }{ 4 } \). Find the probability that exactly 3 of the 5 components tested survive.

Suppose two coins are tossed once. If X denotes the number of tails,
(i) write down the sample space
(ii) find the inverse image of 1
(iii) the values of the random variable and number of elements in its inverse images

Two fair coins are tossed simultaneously (equivalent to a fair coin is tossed twice). Find the probability mass function for number of heads occurred.

If the probability mass function f(x) of a random variable X is

find (i) its cumulative distribution function, hence find
(ii) P(X ≤ 3) and,
(iii) P(X ≥ 2)

If X is the random variable with distribution function F(x) given by,
\(F(x)=\begin{cases} \begin{matrix} 0 & x<0 \end{matrix} \\ \begin{matrix} x & 0\le x<1 \end{matrix} \\ \begin{matrix} 1 & 1\le x \end{matrix} \end{cases}\) 
then find
(i) the probability density function f(x)
(ii) P(0.2 ≤ X ≤ 0.7)

Find the mean and variance of a random variable X , whose probability density function is \(f(x)=\begin{cases} \begin{matrix} { \lambda e }^{ -2x } & for\ge 0 \end{matrix} \\ \begin{matrix} 0 & otherwise \end{matrix} \end{cases}\)

The probability density function of X is given
\(f(x)=\begin{cases} \begin{matrix} { Ke }^{ \frac { -x }{ 3 } } & \begin{matrix} for & x>0 \end{matrix} \end{matrix} \\ \begin{matrix} 0 & \begin{matrix} for & x\le 0 \end{matrix} \end{matrix} \end{cases}\)
Find
(i) the value of k
(ii) the distribution function.
(iii) P(X <3)
(iv) P(5 ≤X)
(v) P(X ≤ 4)

If the probability that a fluorescent light has a useful life of at least 600 hours is 0.9, find the probabilities that among 12 such lights
(i) exactly 10 will have a useful life of at least 600 hours
(ii) at least 11 will have a useful life of at least 600 hours
(iii) at least 2 will not have a useful life of at least 600 hours.

A random variable X has the following probability mass function

Find
(i) P(2 < X < 6)
(ii) P(2 ≤ X < 5)
(iii) P(X ≤4)
(iv) P(3 < X )

The probability density function of random variable X is given by \(f(x)=\begin{cases} \begin{matrix} k & 1\le x\le 5 \end{matrix} \\ \begin{matrix} 0 & otherwise \end{matrix} \end{cases}\) Find
(i) Distribution function
(ii) P(X < 3)
(iii) P(2 < X < 4)
(iv) P(3 ≤ X )