Question
In: Statistics and Probability
Given the following discrete system, find the following x 3 4 5 6 7 P (x)...
Given the following discrete system, find the following
| x | 3 | 4 | 5 | 6 | 7 |
| P (x) | .4 | .2 | .2 | .1 | .1 |
a. E(X)
round to one decimal
b. The Variance
round to two decimals
c. Standard deviation
round to two decimals
d. find P(x ? 5)
round to one decimal using leading zeros
e. find P (x > 4)
round to one decimal using leading zeros
Solutions
Expert Solution
Solution :
From given table,
a ) E(x) = 
x * P(x)
= 3 * 0.4 + 4 * 0.2 + 5 * 0.2 + 6 * 0.1 + 7 * 0.1
= 1.2 + 0.8 + 1.0 + 0.6 + 0.7
= 4.3
= E(x) = 4.3
x2 * P(x) =
32 * 0.4 + 42 * 0.2 + 52 * 0.2 +
62 * 0.1 + 72 * 0.1
x2 * P(x) = 3.6 + 3.2
+ 5 + 3.63 + 4.9 = 20.33
V(x) = x2 * P(x) - ()2 = 20.33 -
(4.3)2 = 20.33 - 18.49 = 1.84
b ) Variance = 1.84
c ) Standard deviation = 
variance = 1.84 = 1.36
x2 * P(x) =
32 * 0.4 + 42 * 0.2 + 52 * 0.2 +
62 * 0.1 + 72 * 0.1
x2 * P(x) = 3.6 + 3.2
+ 5 + 3.63 + 4.9 = 20.33
V(x) = x2 * P(x) - ()2 = 20.33 -
(4.3)2 = 20.33 - 18.49 = 1.84
Variance = 1.84
Standard deviation = variance = 1.84 = 1.36
d ) P(x ? 5)
= P(X = 3) + P(X = 4)+ P(X = 5)
= 0.4+0.2+0.2
= 0.8
Probabilty = 0.8
e ) P (x > 4)
= P(X = 5) + P(X = 6)+ P(X = 7)
= 0.2+ 0.1+ 0.1
= 0.4
Probabilty = 0.4
orchestra answered 2 years agoRelated Solutions
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