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Chapter 4: Q. 73 (page 288)

Complete the PDF and answer the questions.

a. Find the probability thatx=2.

b. Find the expected value.

Short Answer

Expert verified

(a) Px=2=0.1.

(b) The expected value is1.6.

Step by step solution

01

Given information (part a)

02

Explanation

X
Px
X.Px
0
0.3
0
1
0.2
0.2
2
0.1
0.2
3
0.4
1.2
Total1
1.6

Px=0+Px=1+Px=2+Px=3=10.3+0.2+Px=2+0.4=1Px=2=1-0.9Px=2=0.1

The sum of all probabilities for a random variable is1. By this concept, we got the Probability ofx=2.

03

Given information (part b)

04

Explanation (part b)

X
PX
X.Px
0
0.3
0
1
0.2
0.2
2
0.1
0.2
3
0.4
1.2
Total1
1.6

Ex=∑xPX=xEx=0×Px=0+1×Px=1+2×Px=2+3×Px=3Ex=0×0.3+1×0.2+2×0.1+3×0.4Ex=1.6

Thus, the expected value is1.6.

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