1.A random variable x has the following probability distribution. Determine the expected value of x.

x f(x)

0 0.03

1 0.12

2 0.3

3 0.2

4 0.35

2.random variable x has the following probability distribution. Determine the variance of x.

x f(x)

0 0.06

1 0.09

2 0.3

3 0.2

4 0.35

3.A random variable x has the following probability distribution. Determine the standard deviation of x.

x f(x)

0 0.02

1 0.13

2 0.3

3 0.2

4 0.35

4.A warehouse receives orders for a particular product on a regular basis. When an order is placed, customers can order 3, 4, 5, ..., 22 units of the product. Historical data suggest that the size of any given order is equally likely to be of any of these sizes. Let X denote the size of an order.

Find the probability that a customer orders at most five units.

5.A warehouse receives orders for a particular product on a regular basis. When an order is placed, customers can order 3, 4, 5, ..., 28 units of the product. Historical data suggest that the size of any given order is equally likely to be of any of these sizes. Let X denote the size of an order.

Find the probability that a customer orders exactly five units.

6.A warehouse receives orders for a particular product on a regular basis. When an order is placed, customers can order 3, 4, 5, ..., 23 units of the product. Historical data suggest that the size of any given order is equally likely to be of any of these sizes. Let X denote the size of an order.

Find the probability that a customer orders at least five units.

7.A customer service center receives a wide variety of calls for a manufacturer, but 0.17 of these calls are warranty claims. Assume that all calls are independent and that the probability of each call being a warranty claim is 0.17. Let X denote the number of warranty claims received in the first 17 calls.

Calculate P(X=4).

8.A customer service center receives a wide variety of calls for a manufacturer, but 0.14 of these calls are warranty claims. Assume that all calls are independent and that the probability of each call being a warranty claim is 0.14. Let X denote the number of warranty claims received in the first 16 calls.

Find the variance of X.

9.A customer service center receives a wide variety of calls for a manufacturer, but 0.16 of these calls are warranty claims. Assume that all calls are independent and that the probability of each call being a warranty claim is 0.16. Let X denote the number of warranty claims received in the first 13 calls.

Calculate P(X=0).

10.A customer service center receives a wide variety of calls for a manufacturer, but 0.14 of these calls are warranty claims. Assume that all calls are independent and that the probability of each call being a warranty claim is 0.14. Let X denote the number of warranty claims received in the first 16 calls.

Calculate P(X>1).

QUESTION 11

A customer service center receives a wide variety of calls for a manufacturer, but 0.1 of these calls are warranty claims. Assume that all calls are independent and that the probability of each call being a warranty claim is 0.1. Let X denote the number of warranty claims received in the first 10 calls.

Calculate P(X<3).

QUESTION 12

A customer service center receives a wide variety of calls for a manufacturer, but 0.09 of these calls are warranty claims. Assume that all calls are independent and that the probability of each call being a warranty claim is 0.09. Let X denote the number of warranty claims received in the first 16 calls.

Find the expected value of X.

QUESTION 13

Customers arrive at a bank according to a Poisson process having a rate of 2.14 customers per hour. Suppose we begin observing the bank at some point in time.

What is the standard deviation of the number of customers that arrive in the first 1.2 hours?

QUESTION 14

Customers arrive at a bank according to a Poisson process having a rate of 2.42 customers per hour. Suppose we begin observing the bank at some point in time.

What is the probability that 3 customers arrive in the first 1.8 hours?

QUESTION 15

Customers arrive at a bank according to a Poisson process having a rate of 2.14 customers per hour. Suppose we begin observing the bank at some point in time.

What is the expected value of the number of customers that arrive in the first 1.2 hours?

QUESTION 16

Customers arrive at a bank according to a Poisson process having a rate of 1.94 customers per hour. Suppose we begin observing the bank at some point in time.

What is the probability that 1 or fewer customers arrive in the first 1.4 hours?

QUESTION 17

Customers arrive at a bank according to a Poisson process having a rate of 2.3 customers per hour. Suppose we begin observing the bank at some point in time.

What is the probability that at least 3 customers arrive in the first 1.3 hours?