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X157Pr(X x)0.50.350.10.05a)What is the probability that X is at most 6.7?b)What is the probability that X is at least 6.7?Determine the expected value of X, i.e. mean of Xc)Determine the variance of X.d)

Question
X
1
5
7
Pr(X x)
0.5
0.35
0.1
0.05
a)
What is the probability that X is at most 6.7?
b)
What is the probability that X is at least 6.7?
Determine the expected value of X, i.e. mean of X
c)
Determine the variance of X.
d)
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X 1 5 7 Pr(X x) 0.5 0.35 0.1 0.05 a) What is the probability that X is at most 6.7? b) What is the probability that X is at least 6.7? Determine the expected value of X, i.e. mean of X c) Determine the variance of X. d)

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Step 1

The given probability distribution is shown below:

X
Р(Х-х)
1
0.5
3
0.35
5
0.1
7
0.05
Total
1
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X Р(Х-х) 1 0.5 3 0.35 5 0.1 7 0.05 Total 1

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Step 2

a.

The probability that X is at most 6.7 is obtained as follows:

P(XS6.7) P(X-1) + P(X=3)+ P(X=5)
0.50.350.1
=0.95
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P(XS6.7) P(X-1) + P(X=3)+ P(X=5) 0.50.350.1 =0.95

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Step 3

b.

The probability that X is at least 6.7 is ob...

P(x26.7) P(X7)
0.05
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P(x26.7) P(X7) 0.05

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