List of top Statistics Questions asked in MHT CET

A student studies for (X) number of hours during a randomly selected school day. The probability that (X) can take the values, has the following form, where (k) is some constant.
(P(X = x) = 0.2, & if x = 0
kx, & if x = 1 or 2
k(6 - x), & if x = 3 or 4
0, & otherwise )
The probability that the student studies for at most two hours is

Three fair coins numbered 1 and 0 are tossed simultaneously. Then variance Var (X) of the probability distribution of random variable X, where X is the sum of numbers on the uppermost faces, is

The p.m.f. of a random variable X is $P(x) = \begin{cases} \frac{2x}{n(n+1)}, & x = 1, 2, 3, ....... n \\ 0, & \text{otherwise} \end{cases}$, then $E(X)$ is

The distribution function \(F(X)\) of a discrete random variable \(X\) is given by: \[ \begin{array}{c|cccccc} X & 1 & 2 & 3 & 4 & 5 & 6 \\ F(X) & 0.20 & 0.37 & 0.48 & 0.62 & 0.85 & 1 \end{array} \] Then \(P[X = 4] + P[X = 5] =\)

If $f(x) = \begin{cases} 3(1 - 2x^2), & 0<x<1 \\ 0, & \text{otherwise} \end{cases}$ is a probability density function of $X$, then $P\left(\frac{1}{4}<x<\frac{1}{3}\right)$ is