List of top Statistical Science Questions on Probability asked in ICAR AIEEA (PG)

What is the probability of getting a head and a tail in a toss of two coins ?

A random variable X has binomial distribution with n=10 and q=0.3, then variance of X is :

In the Poisson probability distribution, if the value of $\lambda$ is integer then the distribution will be :

If X is random Poisson variate such that P(X=1) = P(X=2). What is the P(X=4) ?

The mean deviation from the mean $m$ in a normal distribution with variance $v^2$ is approximately :

Let the m.g.f. of a random variable \(X\) be of the form \(M_X(t)=\exp\!\left\{3\left(e^t-1\right)\right\}\). What is the value of the kurtosis coefficient \(\beta_2\)?

A multiple-choice test has 30 questions. There are 4 choices for each question. A student who has not studied for the test decides to answer all the questions randomly by guessing the answer to each question. Which of the following probability distributions can be used to calculate the student’s chance of getting at least 20 questions right ?

In a Poisson Distribution, if mean = e, then P(x) is given by ____________.

When Viswanath plays chess, he wins with probability 0.80, loses with probability 0.20. Assume independence, find the probability that Viswanath's first win happens when he plays his third game.

Let A and B are any two events and P(A)= p\(_1\) , P(B)= p\(_2\) and P(A \(\cap\) B)= p\(_3\). What is the value of P\(\left(\frac{\bar{A}}{\bar{B}}\right)\) ?

The probability that both S and T occur, the probability that S occurs and T does not, and the probability that T occurs and S does not are all equal to p. The probability that either S or T occurs is

If X and Y are independent Poisson variates having means 1 and 3 respectively, find the variance of 3X+Y.

Let Y be the number of successes in n independent repetitions of a random experiment having probability of success \(p= 2/3\). If \(n= 3\), compute P (\(2 \le Y\)).

Let the moment generating function (m.g.f) of a random variable is of the form \(M_X(t)=(0.4e^t +0.6)^8\). Find the mean and variance of a random variable Y=3X+2.

The skewness in a binomial distribution will be zero, if :

Three points are taken at random on the circumference of a circle. What is the probability that they will all lie in a semicircle?

Suppose three dice are rolled. Under the condition that no two show the same face, what is the probability that one of the faces is an ace?

The difference between an estimate and the parameter is called :

If n is the number of treatments and r is the number of replications, what is the error degrees of freedom in RBD ?

What is the probability of getting a head and a tail in a toss of two coins ?

A random variable X has binomial distribution with n=10 and q=0.3, then variance of X is :

In the Poisson probability distribution, if the value of $\lambda$ is integer then the distribution will be :

If X is random Poisson variate such that P(X=1) = P(X=2). What is the P(X=4) ?

The mean deviation from the mean $m$ in a normal distribution with variance $v^2$ is approximately :