List of top Statistics Questions on Probability and Uniform Distribution

Let \(X_1,X_2,X_3\) be a random sample of size \(3\) from \(U(1,2)\) distribution. Then \(P(X_{(3)}>1.5)\) equals (rounded off to two decimal places).
A point is chosen at random from a square region whose sides are of \(2\) metres. If the centre of the square is defined to be the point of intersection of its two diagonals, then the probability that the randomly chosen point is closer to the centre of the square than to any of its four corners equals (rounded off to two decimal places).
The probability that a certain electronic component fails when first used is \(0.10\). If it does not fail immediately, the probability that it lasts for one year is \(0.99\). The probability that a new component will last for one year is:
If a fair coin is tossed 5 times, what is the probability of getting exactly 3 heads?
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

The probability mass function of a random variable $X$ is given by: $$ P(X = r) = \begin{cases} \frac{{}^nC_r}{32}, & r = 0,1,2,\dots,n \\ 0, & \text{otherwise} \end{cases} $$ Find: $$ P(X \le 2) $$ 

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
A Poisson variate \( X \) satisfies \( P(X=1) = P(X=2) \). \( P(X=6) \) is equal to
A letter is taken at random from the word "STATISTICS" and another letter is taken at random from the word "ASSISTANT". The probability that they are same letters is
A Poisson variate \( X \) satisfies \( P(X=1) = P(X=2) \). \( P(X=6) \) is equal to
A quadratic equation \( ax^2 + bx + c = 0 \), with distinct coefficients is formed. If \( a,b,c \) are chosen from the numbers 2,3,5, then the probability that the equation has real roots is
A Poisson variate \( X \) satisfies \( P(X=1) = P(X=2) \). \( P(X=6) \) is equal to
A quadratic equation \( ax^2 + bx + c = 0 \), with distinct coefficients is formed. If \( a,b,c \) are chosen from the numbers 2,3,5, then the probability that the equation has real roots is
A letter is taken at random from the word "STATISTICS" and another letter is taken at random from the word "ASSISTANT". The probability that they are same letters is
A Poisson variate \( X \) satisfies \( P(X=1) = P(X=2) \). \( P(X=6) \) is equal to
A quadratic equation \( ax^2 + bx + c = 0 \), with distinct coefficients is formed. If \( a,b,c \) are chosen from the numbers 2,3,5, then the probability that the equation has real roots is
A letter is taken at random from the word "STATISTICS" and another letter is taken at random from the word "ASSISTANT". The probability that they are same letters is
Two balls are selected from two black and two red balls. The probability that the two balls will have no black ball is:
A bag contains 3 red, 4 white and 5 blue balls. If two balls are drawn at random, then the probability that they are of different colours is:
There are 5 positive numbers and 6 negative numbers. Three numbers are chosen at random and multiplied. The probability that the product is a negative number is:
Two fair dice are rolled. Then the probability of getting a composite number as the sum of face values is equal to:
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