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# Refer to Exercise 19.a. Compute the conditional mass ISBN: 9780073401331 38

## Solution for problem 21SE Chapter 2

Statistics for Engineers and Scientists | 4th Edition

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Problem 21SE

Refer to Exercise 19.

a. Compute the conditional mass function PY|X(y|0.06).

b. Compute the conditional mass function PX|Y(x|100).

c. Compute the conditional expectation E(Y | X = 0.06).

d. Compute the conditional expectation  E(X | Y = 100).

Step-by-Step Solution:

Step 1 of 5:

From exercise 19.

The joint probability mass function of tensile strength (y) and additive concentration (x).

 Tensile strength (y) Concentration of additive (x) 100 150 200 0.02 0.05 0.06 0.11 0.22 0.04 0.01 0.08 0.10 0.19 0.06 0.04 0.08 0.17 0.29 0.08 0.04 0.14 0.12 0.3 0.14 0.36 0.5

Step 2 of 5:

a). To compute the conditional mass function Therefore,   = 0.138   = 0.276   = 0.586 Step 3 of 5:

b). To compute the conditional mass function Therefore,  = 0.357   = 0.071   = 0.286   = 0.286 = 0.286.

Step 4 of 5

Step 5 of 5

##### ISBN: 9780073401331

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