KERALA UNIVERSITY Class 4 engineering mathematics 3 probability and random processes Question Paper 2020

Practice authentic previous year questions for better exam preparation.

Sample Questions

A continuous random variable $X$ has a pdf $f(x)=3 x^{2}, 0 \leq x \leq 1$, find $a$ and $b$ such that $P[X \leq a]=P[X>a]$ and $P[X>b]=0.05$.
Find the mean and variance of the number of heads when 3 coins are tossed.
If $X$ is uniformly distributed in $\left[-\frac{5}{4}, \frac{5}{4}\right]$, find $P\left[X<\frac{1}{2}\right]$.
Find the mean and standard deviation of the normal distribution $f(x)=c e^{\frac{-\left(x^{2}-6 x+4\right)}{24}} ;-\infty<x<\infty$.
The joint density of $X$ and $Y$ is given by $f(x, y)=\left\{\begin{array}{ll}k e^{-(2 x+3 y)} ; x>0, y>0 \\ 0, & ; \text { elsewhere }\end{array}\right.$. Find $k$. Are $X$ and $Y$ independent?