A stock will have a loss of 11.5% in a bad economy, a return of 11.3% in a normal economy, and a return of 31% in a hot economy. There is a 29% probability of a bad economy, a 32% probability of a normal economy and a 39% probability of a hot economy. What is the variance of the stock's returns

Variance = 0.030096 or 3.0096% rounded off to 3.01%

Explanation:

To calculate the variance of the stock's returns, we first need to calculate the expected return on the stock. The expected return on the stock can be calculated by multiplying the stock return in each scenario by the probability of that scenario and taking a sum of the answers for each scenario.

Expected return of stock rE=  pA * rA  +  pB * rB  + ... + pN * rN

Where,

Expected return of stock rE = 0.29 * -0.115  +  0.32 * 0.113  +  0.39 * 0.31

Expected return of stock rE = 0.12371 or 12.371%

Variance = ∑ p * (r - rE)²

Variance = 0.29 * (-0.115 - 0.12371)^2  +  0.32 * (0.113 - 0.12371)^2  +  

0.39 * (0.31 - 0.12371)^2

Variance = 0.030096 or 3.0096% rounded off to 3.01%

a recipe serves 8 people, and calls for 5 lbs of apples and 2 cups of flour. you want to prepare it for 24 people. divide 24 by 8 to get 3, and then multiply your ingredients by 3.

so for 24 people, you'll need 15 lbs of apples, and 6 cups of flour.

being born in poverty would limit the people's chances, opportunities and benefits.

this happen because of several things, such as:

- poor people tend to gain less access to good education and nutrition. this mean that their chance to obtain high paying jobs would also be limited.

- poor people tend to socialize with other poor people while the rich tend to socialize with other rich people. this means that simply throguh their social circle, rich people would have more business opportunities compared to the poor people.

- rich people tend to have more capital in their disposal. this would benefit them in business since it is far easier for them to fund their business operation compared to poor people.