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# Find the missing values of the following probability distribution

Subject: Mathematics    / Statistics
Question
m118 Homework 10 (5.2)
Name:
Based on concepts from Section 5.2 (Expected Value, Variance, and Standard Deviation)
1. [a] Find the missing values of the following probability distribution.
[b] Find the variance.
[c] Find the standard deviation .
x 8 Pr[x] x?Pr[ x] 0.2 2 0.1 5 0.5 3
0.4
E[x]= 2.5

2. A basketball player makes each free throw with a probability of 0.75. If this player attempts 75 shots, find the
expected value and standard deviation for the number of made free throws.

3. An experiment consists of rolling a pair of dice 42 times. If the random variable X is defined as the number of
times the dice produce a sum larger than 8:
[a] What is the expected value of X? [b] What is the standard deviation?

4. A jar contains 3 nickels and 2 dimes. You reach in and randomly select 2 coins. Let X represent the value of the two
coins in cents. Find the expected value and standard deviation of X.

5. There are 10 books on a shelf. Eight are fiction and two are non-fiction. Three books are selected at random. A random variable is defined to be the number of non-fiction books selected. Find the expected value and standard deviation for this experiment.

6. Suppose 10% of all people are left-handed. If 300 people are selected at random, find the expected value and
standard deviation for the number of left-handed people in the sample.

7. In a carnival game the probability that you win \$100 is 0.04, the probability that you win \$10 is 0.30, and the probability that you lose \$5 is 0.66. What is your expected return per game? (i.e. find the expected value)?