ASSIGNMENT C
SPRING 2023
- Let
over , where is a positive integer. Determine the value of the constant (in terms of )that makes this a probability density function.
2.Suppose we have a probability density function defined in as Verify that this is indeed a probability density function.
3.For the density function given in problem2, determine the cumulative distribution function.
4.Suppose we have a probability density function defined as
in . Find the expected value.
5.Suppose we have a probability density function defined as in . Find the variance.
6.Suppose the cumulative distribution function of a continuous random variable is given as
in . Determine its expected value.
R PART
7.The probability that a person carries a certain gene is 0.1. What is the probability that the third person with the gene would be the tenth person tested?
8.Graph the distribution you obtained in problem 7.
9.In a group of 1000 components, 65 are defective. In a sample of 200 components selected at random and without replacement, what is the probability that 15 will be defective?
10.Graph the distribution you obtained in problem 9.