Consider a discrete probability distribution function:

p(x)=C(9,x)/165 which is valid for the values of X = 1, 2, 6, 7.

Complete the following probability distribution table. (Enter your probabilities to 4 decimal places.)

Complete the following probability distribution table. (Enter your probabilities to 4 decimal places.)

Value ofX	Probability
x=1
x=2
x=6
x=7

1. Determine P(X=3). (Give your answer to 4 decimals.)

2. Determine P(X 3) (Give your answer to 4 decimals.)

3. Determine the expected value of X. (Give your answer to 2 decimals.)

4. Fill in the blanks for the formula you would use to calculate the variance of X.

²= ( - )² + ( - )²+ ( - )²+ ( - )²

5. A CEO is considering buying an insurance policy to cover possible losses incurred by marketing a new product. If the product is a complete failure, a loss of $720,000 would be incurred; if it is only moderately successful, a loss of $162,000 would be incurred. Insurance actuaries have determined that the probabilities that the product will be a failure or only moderately successful are 0.02 and 0.08, respectively. Assuming that the CEO is willing to ignore all other possible losses, what premium should the insurance company charge for a policy in order to break even?

6. You can insure a $16,000diamond for its total value by paying an annual premium ofDdollars.If the probability of loss in a given year is estimated to be 0.02, what is the minimum premium that the insurance company should charge if it wants the expected profit from this insurance policy to equal at least $2,130annually?D=