please answer i only have 3-4 minutes !!!

On any given day, a bike shop sells either 0, 1, 2, or 3, bikes, with probabilities 0.3, 0.4, 0.2, and 0.1 respectively.

Suppose they make a profit of $400 from each bike sold, but they have a fixed cost of $400 per day for rent and salaries at the small dealer.

Let the random variable X = the net profit per day. (i.e., the profit from the sale of bicycles minus the fixed cost).

a) Develop a probability distribution for the net profit per day. What are the X and f(x) values?

b) Show that your probability distribution satisfies the conditions for a discrete probability distribution. In other words, describe in words why the probability distribution that you created is a valid one.

c) Calculate the expected value of the probability distribution. Interpret what this means in words.

Assume that the risk-free rate is 4.1 percent. If a stock has a beta of 0.5 and a required rate of return of 10.1 percent, and the market is in equilibrium, what is the return on the market portfolio? Show your answer to the nearest .1% using whole numbers (e.g., enter 14.1% as 14.1 rather than .141). Your Answer?

An analyst has estimated how a stock's return will vary depending on what will happen to the economy. If a Recession economy occurs (.1 probability), expected return is -60%. If a Below Average economy occurs (.2 probability), expected return is -10%. If an Average economy occurs (.4 probability), expected return is 15%. If an Above Average economy occurs (.2 probability), expected return is 40%. If a Boom economy occurs (.1 probability), expected return is 90%.
What is the expected return and standard deviation on the companys stock?

Genetics: According to genetic theory, the blossom color in the second generation of a certain cross of sweet peas should be red or white. Each plant has a probability of 3/4 of having red blossoms, and the blossom colors of separate plants are independent. You are testing 10 pea plants for their blossoming behavior.

a. Explain why the event “having red blossom” in this specific context is binomial using the four characteristics of a binomial setting.

b. What is the probability that all 10 pea plants do not have red blossoms?

c. What is the probability that at least one of the ten pea plants has red blossoms? (Hint: Use part c) to answer this question)

d. Based on the probability that you computed in part c), would you question the true probability of pea plants developing a red blossom? Explain your answer.

            You have decided to open a restaurant in Huntington. The following table gives the payoffs based on two states of nature, favorable and unfavorable demand. You     believe that the probability of a favorable market is 0.8. You can open any one of        three different sizes of restaurant.     

            You have decided to do some marketing research (using the skills that you learned). If the marketing research is positive (probability = .7), then the probability of favorable demand goes to .95. If the marketing research is negative (shows weak demand) (probability of .3), then the probability of favorable demand goes to .40.

1. Using all of the information, what should you do? Provide calculations.

2. What is the expected value of perfect information?

3. What is the expected value of sample information?

Say we have a continuous random variable X with density f(x) = c (1+x³) (where c is a constant) with support S_x = [0,3]

a. What value of c will make f(x) a valid probability density function?

b. What is the probability that X=2? What is the probability that X is greater than 2?

Now say we have an infinite sequence of independent random variables X_i (that is to say X₁, X₂, X₃, ....)  with density f(x) stated earlier.

c. What is the probability that the first random variable/trial to be greater than 2 is on the 10

trial (first 9 trials are less than 2 and the 10 trial is greater than 2)?

d. What is the probability that it will take less than 10 random variables/trials before we see a

trial that is greater than 2?

The time between car arrivals at an inspection station follows an exponential distribution with V (x) = 22 minutes.
1) Calculate the probability that the next car will arrive before the next 10 minutes.
2) Calculate the probability of receiving less than 5 cars during the next hour
3) If more than half an hour has passed without a car being presented, what is the probability that the employee will remain unemployed for at least 10 minutes?
4) If the employee wants to take a break, what is the maximum time that the break must last so that the probability of the next client arriving and not finding the employee in his position is less than or equal to 5%?
5) If we take the times between arrivals for the next 40 minutes and calculate the average, what is the probability that the average time is less than 20 minutes? Under 22 minutes?

Suppose gene A is on the X chromosome, and genes B, C and D are on three different autosomes. Thus, A- signifies the dominant phenotype in the male or female. An equal situation holds for B-, C- and D-. The cross AA BB CC DD (female) x aY bb cc dd (male) is made.

A) probability of obtaining A- individual in F1

B) probability of obtaining an a male in the F1 progeny

C) Probability of A- B- C- D- female in F1

D) How many different F1 genotypes are there?

E) Probability of F2 individuals will be heterozygous for the four gens?

F) Determine a probability of each of the following types in the F2     individuals  

(1) A- bb CC dd (female);  

(2) aY BB Cc Dd (male);  

(3) AY bb CC dd (male);  

(4) aa bb Cc Dd (female)

Say we have a continuous random variable X with density function f(x)=c(1+x3) (where c is a constant)with support SX =[0,3].

a.) What value of c will make f(x) a valid probability density function.

b. )What is the probability that X=2? What is the probability that X is greater than 2?

Now say we have an infinite sequence of independent random variables Xi (that is to say X1, X2, X3, ....) with density f(x) stated earlier.

c. What is the probability that the first random variable/trial to be greater than 2 is on the 10 trial (first 9 trials are less than 2 and the 10 trial is greater than 2) ?

d. What is the probability that it will take less than 10 random variables/trials before we see a trial that is greater than 2?

Suppose in a local Kindergarten through 12^th grade (K - 12) school district, 53 percent of the population favor a charter school for grades K through five. A simple random sample of 600 is surveyed. Calculate the following using the normal approximation to the binomial distribution. (Round your answers to four decimal places.)

(a) Find the probability that less than 250 favor a charter school for grades K through 5.


(b) Find the probability that 315 or more favor a charter school for grades K through 5.


(c) Find the probability that no more than 290 favor a charter school for grades K through 5.


(d) Find the probability that there are fewer than 275 that favor a charter school for grades K through 5.


(e) Find the probability that exactly 300 favor a charter school for grades K through 5.

An industrial sewing machine uses ball bearings that are targeted to have a diameter of 0.73 inch. The lower and upper specification limits under which the ball bearing can operate are 0.715 inch​ (lower) and 0.745 inch​ (upper). Past experience has indicated that the actual diameter of the ball bearings is approximately normally​ distributed, with a mean of 0.734 inch and a standard deviation of 0.006 inch. Suppose a random sample of 22 ball bearings are selected. Complete parts​ (a) through​ (e). What is the probability that the sample mean is between the target and the population mean of 0.734​? What is the probability that the sample mean is between the lower specification limit and the​ target? What is the probability that the sample mean is greater than the upper specification​ limit? What is the probability that the sample mean is less than the lower specification​ limit? The probability is 92​% that the sample mean diameter will be greater than what​ value?