代做ECE2191 Probability Models in Engineering Example 1帮做R编程

ECE2191

Probability Models in Engineering

Example 1

1 (10 points) From a drawer that contains 10 pair of matching gloves, six gloves are selected randomly. Let X be the number of pairs of matching gloves obtained. Find the probability mass function of X.

2 (10 points) An urn contains five balls, two of which are marked $1, two $5, and one $15. A game is played in which a player pays $10 to play, and selects two balls from the urn. The player wins the sum of the amounts marked on the selected balls. Find the expectation and variance of the net gain.

3 (20 points) Let the joint probability mass function (PMF) of discrete random variables X and Y be given by

Determine:

1. the value of the constant k

2. the marginal probability mass functions of X and Y

3. P(X> 1Y =1)

4. E(X) and E(Y)

4 (10 points) Let X be a random number from (0,1). Find the probability density function of Y 1/X.

(Hint. Use the relationship between CDF and PDF)

5 (10 points) A point is selected at random on a line segment of length I. What is the probability that none of the two segments is smaller than l/3?

6 (20 points) If 65 percent of the population of a large community is in favor of a proposed rise in school taxes, approximate the probability that a random sample of 100 people will contain

1. at least 50 who are in favor of the proposition;

2. between 60 and 70 inclusive who are in favor;

3. fewer than 75 in favor.

(Hint: Number of people in favor of proposed tax can be modeled as a Binomial R.V., also note  = 4.76)