CUET Mathematics: Applied MathematicsProbability Distribution. Free, no login required.

The variance of the Binomial Distribution $B\left(5, \frac{1}{4}\right)$ is:

A shopkeeper wants to check the average number of cars sold per call. Past record of sales is shown below:

The expected number of cars sold is :

If the mean of a binomial distribution is 12 and its standard deviation is 2, then the number of trials is :

If the probability distribution of X is :

Then variance is equal to :

If a random variable X follows binomial distribution with mean 5 and variance $\frac{5}{2}$, then $P(X \leq 9)$ is :

Which of the following statements are correct ?

(A) $\text{var}(aX + b) = a^2 \text{var}(X)$

(B) $\text{var}(X) = E(X^2) - \{E(X)\}^2$

(C) $E(aX + b) = aE(X) + b$

(D) $E(X) = \sum_{i=1}^{n} p_i x_i^2$

Choose the correct answer from the options given below :

In binomial distribution with $n = 10$ and $P = \frac{1}{3}$, the probability of the event that unequal number of failures and successes occur is :

The probability distribution of a random variable X is given below :

Then, $\text{Var}\left(\frac{X}{2}\right)$ is :

If X has a Poisson distribution such that $P(X = 1) = P(X = 2)$ then $P(X = 3)$ is :

A discrete random variable X has the following probability distribution :

The value of b is :

A discrete random variable X takes the values 0, 1, 2, 3, 4 and its mean is 1.6. If $P(X=1) = 0.4$, $P(X=4) = P(X=2)$ and $P(X=3) = 2P(X=2)$, then $P(X=0)$ is :

A telephone exchange receives on an average 5 calls per minute. The probability of receiving 3 or less calls per minute is :

Match List - I with List - II.

Choose the correct answer from the options given below :

If the sum and product of the mean and variance of a binomial distribution are 18 and 72 respectively, then the probability of obtaining atmost one success is

Between 3 p.m. and 5 p.m. the average number of phone calls per minute coming into the helpline desk of a bank is 5. The probability that during one particular minute there will be only one phone call is :

Match List I with List II

Choose the correct answer from the options given below:

If the probability distribution of a discrete random variable $X$ is given as

Then the value of $k$ is:

If the probability distribution of a random variable X is given as

Then the mean of X is