A stock has a required return of 10%, the risk-free rate is 4.5%, and the market risk premium is 2%.

1. What is the stock's beta? Round your answer to two decimal places.
2. If the market risk premium increased to 6%, what would happen to the stock's required rate of return? Assume that the risk-free rate and the beta remain unchanged. Do not round intermediate calculations. Round your answer to two decimal places.
   1. If the stock's beta is equal to 1.0, then the change in required rate of return will be less than the change in the market risk premium.
   2. If the stock's beta is greater than 1.0, then the change in required rate of return will be greater than the change in the market risk premium.
   3. If the stock's beta is less than 1.0, then the change in required rate of return will be greater than the change in the market risk premium.
   4. If the stock's beta is greater than 1.0, then the change in required rate of return will be less than the change in the market risk premium.
   5. If the stock's beta is equal to 1.0, then the change in required rate of return will be greater than the change in the market risk premium.

   Stock's required rate of return will be ____ %.

Plot using RStudio

Consider a binomial random variable, X.

i. Plot the pmf of X ∼Bin(n = 10, p = 0.3).

ii. Plot the pmf of X ∼Bin(n = 10, p = 0.7).

iii. Plot the pmf of X ∼Bin(n = 100, p = 0.3).

iv. What happens to the shape of the pmf of X ∼Bin(n, p) when p gets larger?

v. What happens when n gets larger

A bank wants to know if the enrollment on their website is above 30%. They test the null hypothesis that the proportion is 0.3, and the alternative that the proportion is greater than 0.3. After obtaining a sample, they fail to reject the null hypothesis. Later they find out that 30% of all customers enrolled. Answer whether there was a Type I error, Type II error, or neither error was made.

Group of answer choices

Type I error

Type II error

Neither error was made

A large group of mice is kept in a cage having compartments​ A, B, and C. Mice in compartment A move to B with probability 0.3 and to C with probability 0.4. Mice in B move to A or C with probabilities 0.35 and 0.55​, respectively. Mice in C move to A or B with probabilities 0.3 and 0.2​, respectively. Find the​ long-range prediction for the fraction of mice in each of the compartments.

The​ long-range prediction for the fraction of mice is___in compartment​ A,___in compartment​ B,____in compartment​ C, ____

Assume Raoult's Law applies to a binary mixture of water and methanol at 70 C.

a) Which species should be considered species (a)? Why?

b) Prepare a Pxy diagram for this mixture

c) What is the composition of the vapor in equilibrium with liquid at x_i for methanol of 0.3?

d) What is the composition of the liquid in equilibrium with vapor at y_i for water of 0.3?

For parts (c) and (d), determine these composition values analytically. Then confirm that they are correct on the Pxy diagram you created in part (b).

A road perpendicular to a highway leads to a farmhouse located 22 mile away. An automobile traveling on the highway passes through this intersection at a speed of 55mph.55mph.

How fast is the distance between the automobile and the farmhouse increasing when the automobile is 11 miles past the intersection of the highway and the road?

The distance between the automobile and the farmhouse is increasing at a rate of  miles per hour.

A researcher claims that the average wind speed in his city is 10 miles per hour. In a random sample of 36 days, you found the average speed of wind is 10.2 with a standard deviation of 0.8 miles per hour. At α=0.05 is there enough evidence to say that the average is greater than the researcher’s claim. Show your work by using hypothesis testing.

A train starting at noon, travels north at 40 miles per hour. Another train starting from the same point at 2 PM travels east at 50 miles per hour. Find, to the nearest mile per hour, how fast the two trains are separating at 3 PM. How fast the trains are separating after long time?

In 10 test runs, a truck operated for 8, 10, 10, 7, 9, 12, 10, 8, 7, and 9 miles with one gallon of a certain gasoline. Is this evidence at the 0.05 level of signifcance that the truck is not operating at an average of 11.5 miles per gallon with this gasoline? What assumptions must be satised in order for the procedure you used to analyze these data to be valid?