Respuesta :
Answer:
a). The mean = 1000
The variance = 999,000
The standard deviation = 999.4999
b). 1000 times , loss
Step-by-step explanation:
The mean of geometric distribution is given as , [tex]$\mu = \frac{1}{p}$[/tex]
And the variance is given by, [tex]$\sigma ^2=\frac{q}{p^2}$[/tex]
Given : [tex]$p=\frac{1}{1000}$[/tex]
= 0.001
The formulae of mean and variance are :
[tex]$\mu = \frac{1}{p}$[/tex]
[tex]$\sigma ^2=\frac{q}{p^2}$[/tex]
[tex]$\sigma ^2=\frac{1-p}{p^2}$[/tex]
a). Mean = [tex]$\mu = \frac{1}{p}$[/tex]
= [tex]$\mu = \frac{1}{0.001}$[/tex]
= 1000
Variance = [tex]$\sigma ^2=\frac{1-p}{p^2}$[/tex]
= [tex]$\sigma ^2=\frac{1-0.001}{0.001^2}$[/tex]
= 999,000
The standard deviation is determined by the root of the variance.
[tex]$\sigma = \sqrt{\sigma^2}$[/tex]
= [tex]$\sqrt{999,000}$[/tex] = 999.4999
b). We expect to have play lottery 1000 times to win, because the mean in part (a) is 1000.
When we win the profit is 500 - 1 = 499
When we lose, the profit is -1
Expected value of the mean μ is the summation of a product of each of the possibility x with the probability P(x).
[tex]$\mu=\Sigma\ x\ P(x)= 499 \times 0.001+(-1) \times (1-0.001)$[/tex]
= $ 0.50
Since the answer is negative, we are expected to make a loss.
The mean, variance, and standard deviation will be 1000, 999000, and 999.50 respectively.
Based on the information given, the mean will be:
= 1/p = 0.001 = 1000
The variance will be calculated as:
= (1 - 0.001) / 0.001²
= 999,000
The standard deviation will be;
= ✓999000
= 999.50
Lastly, the number of times that the person will expect to play before winning will be 1000 times and when there's a loss, the amount will be -1 and a winning brings a profit of $499.
Learn more about mean on:
https://brainly.com/question/20118982
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