2. Engineering Mathematics

Probability Theory — Quiz

Test your understanding of probability theory with 5 practice questions.

Practice Questions

Question 1

A continuous random variable $X$ has a probability density function (PDF) given by $f(x) = k(x+1)$ for $0 \le x \le 2$, and $f(x) = 0$ otherwise. What is the value of the constant $k$?

Question 2

In a binomial distribution, if $n$ is the number of trials and $p$ is the probability of success on a single trial, what is the standard deviation of the number of successes?

Question 3

The joint probability mass function of two discrete random variables $X$ and $Y$ is given by $P(X=x, Y=y) = c(x+y)$ for $x=1, 2$ and $y=1, 2$. What is the value of the constant $c$?

Question 4

If $X$ is a Poisson random variable with parameter $\lambda = 2$, what is $P(X=1)$?

Question 5

What is the definition of the 'moment-generating function' (MGF) for a random variable $X$?