Answer:
The probability distribution of x is
Profits in millions (x) Probability of getting contract (P(x))
$10 0.15
$ 5 0.30
$ 2 0.45
$ 0 0.10
The mean is [tex]E(X) = 3.9 millions [/tex]
The standard deviation is [tex]s = 3.01 \ millons [/tex]
Step-by-step explanation:
Generally the probability distribution of x is
Profits in millions (x) Probability of getting contract (P(x))
$10 0.15
$ 5 0.30
$ 2 0.45
$ 0 0.10
Generally the mean is mathematically represented as
[tex]E(X) = x * p(x)[/tex]
=> [tex]E(X) = [10 * 0.15 ] + [5 *0.30 ] + [2 * 0.45 ] + [0 * 0.10] [/tex]
=> [tex]E(X) = 3.9 millions [/tex]
Now
[tex] E(X^2) = x^2 * p(x)[/tex]
=> [tex] E(X^2) = (10 ^2 * 0.15) + (5 ^2 * 0.30) +(2 ^2 * 0.45) + (0 * 0.10)[/tex]
=> [tex] E(X^2) = 24.3 [/tex]
Gnerally the variance is mathematically represented as
[tex]V(X) = E(X^2) - [E(X)]^2[/tex]
=> [tex]V(X) = 24.3 - 3.9^2[/tex]
=> [tex]V(X) = 9.09 [/tex]
Gnerally the standard deviation is mathematically represented as
[tex]s = \sqrt{V(X)}[/tex]
=> [tex]s = \sqrt{9.09[/tex]
=> [tex]s = 3.01 [/tex]
