Answered

Find the best solutions to your questions at Westonci.ca, the premier Q&A platform with a community of knowledgeable experts. Connect with a community of experts ready to provide precise solutions to your questions on our user-friendly Q&A platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.

For 40 values of the variable x, it is given that E(x-c)² = 3099.2, where is a constant. The standard deviation of these values of x is 3.2.

(i) Find the value of E(x-c).

Sagot :

LammettHash

If c is a constant, then

E[X - c] = E[X] - E[c]

… = E[X] - c

and

E[(X - c)²] = E[X² - 2cX + c²]

… = E[X²] - 2c E[X] + E[c²]

… = E[X²] - 2c E[X] + c²

Recall the definition of variance:

Var[X] = E[(X - E[X])²]

… = E[X² - 2X E[X] + E[X]²]

… = E[X²] - E[2X E[X]] + E[E[X]²]

… = E[X²] - 2E[X] E[X] + E[X]²

… = E[X²] - E[X]²

The standard deviation of X is 3.2, so Var[X] = 3.2² = 10.24.

By this definition,

Var[X - c] = E[(X - c)²] - E[X - c]²

but again because c is constant,

Var[X - c] = Var[X]

This is because

Var[X - c] = E[(X - c)²] - E[X - c]²

… = E[X² - 2cX + c²] - (E[X] - E[c])²

… = E[X²] - 2c E[X] + E[c²] - E[X]² + 2 E[X] E[c] - E[c]²

… = (E[X²] - E[X]²) - 2c E[X] + E[c]² + 2c E[X] - E[c]²

… = Var[X]

Then

10.24 = 3099.2 - E[X - c]²

⇒   E[X - c]² = 3088.96

⇒   E[X - c] = 55.5784

Thank you for your visit. We are dedicated to helping you find the information you need, whenever you need it. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.