How to find standard deviation of a random variable

Practice Questions

AP Statistics › How to find standard deviation of a random variable

Questions

If $\small X_1$ and $\small X_2$ are two independent random variables with and , what is the standard deviation of the sum, $\small X_1+X_2?$

Consider the discrete random variable $\small X$ that takes the following values with the corresponding probabilities:

$\small X=1$ with $\small P(X=1)=\frac{1}{8}$
$\small X=2$ with $\small P(X=2)=\frac{3}{8}$
$\small X=3$ with $\small P(X=3)=\frac{1}{2}$

Compute the probability $\small P(X\ge2)$ .

Consider the discrete random variable $\small X$ that takes the following values with the corresponding probabilities:

$\small X=1$ with $\small \small P(X=1)=\frac{1}{4}$
$\small X=2$ with $\small \small P(X=2)=\frac{1}{4}$
$\small X=3$ with $\small \small P(X=3)=\frac{1}{4}$
$\small X=4$ with $\small P(X=4)=\frac{1}{4}$

Compute the expected value of the distribution.

The average number of calories in a Lick Yo' Lips lollipop is , with a standard deviation of . The calories per lollipop are normally distributed, so what percent of lollipops have more than calories?

We have two independent, normally distributed random variables $\small X_1$ and $\small X_2$ such that $\small X_1$ has mean $\small 0$ and variance $\small 2$ and $\small X_2$ has mean $\small 0$ and variance $\small 1$ . What is the probability distribution of the difference of the random variables, $\small \small X_1-X_2$ ?

Robert's work schedule for next week will be released today. Robert will work either 45, 40, 25, or 12 hours. The probabilities for each possibility are listed below:

45 hours: 0.3

40 hours: 0.2

25 hours: 0.4

12 hours: 0.1

What is the standard deviation of the possible outcomes?

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