Statistics- A random variable X has the probability density function

Subject: Mathematics    / Statistics
Question
Question 1: A random variable X has the probability density function shown below. Find the expected value of the random variable
Value of X Probability
-3
0.1
2
0.2
5
0.4
7
0.3 Question 2: Two coins are randomly selected from a pocket containing two quarters, one dime, and one nickel. A random variable X is defined as the total value of the two coins selected. Find the expected value (in cents). Question 3: An unfair coin with Pr[H]=0.1 is flipped 71 times. A random variable X is defined as the number of heads that occur. Find the standard deviation. Question 4: A state lottery ticket costs $1. The probability of winning $1,000,000 is 0.0000001, the probability of winning $1,000 is 0.000005, and the probability of winning $10 is 0.0002. Find the expected value (gain or loss) on one ticket. Question 5: Two candidates are running for president; John Democrat and Joe Republican. A recent survey concluded that John Democrat had a probability of 0.46 to win the election. 24 people are interviewed at random about whom they would vote for. A random variable X is defined as the number of people who said they would vote for John Democrat. Find
the expected value of the random variable. Question 6: One cage contains 2 white mice and 3 black ones, and another cage contains 3 white mice and 2 black ones. A cage
is chosen at random and three mice are selected. Find the expected number of white mice in the sample. Question 7: The probability that a woman is widowed or divorced is 0.62. 19 women are interviewed at random. Let the random vairable X be defined as the number of women who are widowed or divorced.
Find the expected
____________
value.
Find the standard deviation. ____________ Question 8: A roulette wheel has 38 slots numbered 00, 0, 1, 2, …, 35, 36. Eighteen of the slots numbered 1 through 36 are red and eighteen are black. The 00 and 0 slots are green. The ball is spun around the wheel until it falls into one of the slots. When a gambler bets $1 on a single number and wins, he gets $36 back (i.e. his net winnings are $35). Find the expected value of this game (in dollars). Question 9: Stereo speakers are manufactured with a probability 0.03 of being defective. 15 speakers are randomly selected. Let X be defined as the number of defective speakers in the sample. Find the expected value. Question 10: Stereo speakers are manufactured with a probability 0.12 of being defective. 19 speakers are randomly selected. Let X be defined as the number of defective speakers in the sample. Find the standard deviation.

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