a) Define your random variables, and use them to express the farmer's net income. A. Apounds of apples sold, , B. Aprice per pound of apples, , C. Apounds of apples sold, , D. Aprice per pound of apples, , b) Find the mean. The mean profit is 62 dollars. c) Find the standard deviation of the net income. The standard deviation is nothing dollars. (Round to two decimal places as needed.) d) Do you need to make any assumptions in calculating the mean? A. Yes; the prices must be independent. B. Yes; the variables must be discrete. C. Yes; the prices must be dependent. D. No; no assumptions are made in calculating the mean. Do you need to make any assumptions in calculating the standard deviation? A. Yes; the prices must be independent. B. Yes; the prices must be dependent. C. Yes; the variables must be discrete. D. No; no assumptions are made in calculating the standard deviation. Click to select your answer(s).

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codiepienagoya codiepienagoya · Answer 1 · 2021-06-17T09:55:31+02:00

Answer:

Please find the complete question in the attached file:

Step-by-step explanation:

For point a:

When X was its random variable of apples, Y the randomized variables of potatoes, then

[tex]\to 100\ X + 50\ Y - 2[/tex]

Your gross profit is represented.

For point b:

The expected value varies as per the random variables:

[tex]\to \mu=100 \mu_{X}+50 \mu_{Y}-2=100(0.5)+50(0.3)-2=\$ 63[/tex]

For point c:

Its variance varies to the square of coefficient (without constants) as well as the standard variance is dependent upon on square root:

[tex]\sigma=\sqrt{100^2\sigma_{X}^2 +50^2 \sigma_{Y}^2}\=\sqrt{10,000(0.2^2) + 2500(0.1^2)} \approx \$20.62[/tex]

For point d:

Yes, because prices are dependent on the apple as well as the prices of potatoes.