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?

Statistics by Geoffrey

ASSIGNMENT C

SPRING 2023

 

  1. 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.