4. Statistics

Continuous Distributions — Quiz

Test your understanding of continuous distributions with 5 practice questions.

Practice Questions

Question 1

Which of the following is NOT a necessary property of the probability density function $f(x)$ for a continuous random variable?

Question 2

Given $X$ has CDF $F(x)=0$ for $x<2$, $F(x)=(x-2)/3$ for $2\le x\le5$, and $F(x)=1$ for $x>5$, what is $P(3\le X\le4)$?

Question 3

If $X\sim N(10,2^2)$, what is $P(7<X<13)$?

Question 4

A population has mean $\mu=5$ and standard deviation $\sigma=3$. For a random sample of size $n=36$, approximate $P(4<\overline X<6)$ using the Central Limit Theorem.

Question 5

If $X\sim N(20,5^2)$, find $k$ such that $P(X<k)=0.975$.