HW2 - Dr. Julie Swenson PDF

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Dr. Julie Swenson...

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PSTAT 5A

S20

Homework 2 1. Unit 2 Self-Assessment Quiz. 2. The diagram below depicts event A and event B inside the sample space, S. Assume that R1, R2, R3 and R4 represent the areas in the individual regions, and together span the area of the entire sample space. For the following questions, use proper notation, i.e. P(______). S

A R2

B R1

R3 R4

If R1 + R3 = P(B) and R1 = P(A and B), write the equivalent probability statement for each of the following: a) R3 + R4 b) R3 c) R1 + R2 + R3 + R4 d) R1 + R2 + R3 3. Use the following table to answer the questions. 19 25 28 34 x P(X≤x) 0.05 0.38 0.44 0.75 a) b) c) d) e)

Find the probability that X is at most 30. Find the probability that X is between (inclusive) 25 and 35. Construct the corresponding pdf. Calculate the mean of X. Calculate the standard deviation of X.

4. Use the following table to answer the questions. -25 -15 -5 5 x P(X=x) a 0.1 0.02 0.27 a) b) c) d) e)

39 1

15 0.09

25 0.06

40 0.01

Find the value of a. What is the probability that X is 25? What is the probability that X is less than 5? What is the probability that X is at least -5? Calculate the expected value of X.

5. According to the Santa Barbara Times, only 65% of gift cards are redeemed. They select 3 gift cards at random. a) Let Gi= ith gift card is redeemed. List all the possible outcomes. b) Find the probability that none of the gift cards are redeemed.

PSTAT 5A

S20

c) Find the probability that exactly one gift card is redeemed, by calculating the sum of the probabilities of the “successful” outcomes. d) Sixty gift cards are now selected at random. Do you think the method you used to calculate 5c should be used to calculate the probability that exactly forty-eight are redeemed? Yes, or no?...