Five males with an​ X-linked genetic disorder have one child each. The random variable x is the number of children among the five who inherit the​ X-linked genetic disorder. Determine whether a probability distribution is given. If a probability distribution is​ given, find its mean and standard deviation. If a probability distribution is not​ given, identify the requirements that are not satisfied. x ​P(x) 0 0.027 1 0.149 2 0.324 3 0.324 4 0.149

2. A fire detector uses 3 sensors with a sensitivity level of 0.8 each (meaning the probability that a sensor will turn on if the room temperature reaches 100oC or more is 0.8). A fire alarm will sound if at least one sensor is on. Suppose Y is a random variable that states the number of sensors that are on, then specify:

a. Possible values for Y!

b. Probability function for random variable Y1

c. Y score and variance.

d. What are the probability of the device providing incorrect information?

Seventy three percent of drivers carry jumper cables in their vehicles. from a random sample of 315 driver

A. What is the probability that exactly 225 carry jumper cables in their vehicle

B. What is the probability that at most 225 carry jumper cables in their vehicle

C. What is the probability that more than 210 carry jumper cables in their vehicle

D. What is the mean value of the number of driver that carry jumper cable in their vehicle

E. What is the standard deviation

1. The number of missed notes by a musician in a symphony is Poisson. Suppose the principle trombonist misses an average of 2 notes per concert, and the 2nd trombonist misses an average of 5 notes per concert.

(a) What is the probability that they miss no notes in a concert?

(b) Suppose a concert requires only one trombonist and there is an even chance either is chosen. What is the probability no notes are missed in that concert?

(c) If no notes were missed, what is the probability that the principle trombonist was playing?

This exercise assumes familiarity with counting arguments and probability.

Kent's Tents has four red tents and three green tents in stock. Karin selects four of them at random. Let X be the number of red tents she selects. Give the probability distribution. (Enter your probabilities as fractions.)

Find

P(X ≥ 2).

(Enter your probability as a fraction.)

P(X ≥ 2) =

A box contains eight chips numbered 1 through 8. You randomly select three at random without

replacement.

(a) What is the probability that the largest chip selected is chip number 5?

(b) What is the probability that you select two odd numbered chips and a even numbered chip?

(c) What is the probability that at least one of the chips is numbered 6 or higher?

Please include any theorems or principles you use in your explanation. Thank you.

You are the financial policy advisor for President Trump/Biden (whoever wins on Tuesday). Based on what we know about the economy today what would you advise the President to do help the economy?

Factors to consider

A) what phase of the business cycle are we in?

B) is main problem inflation or unemployment?

C) What do economic indicators point to? GDP (up/Down) ? Stock market? Housing market? Consumer confidence and spending?

D) Raise or lower taxes?

Using the data you can find and you knowledge of economics as well as your own opinions write a 5 paragraph paper to the winner of the election advising them how to correct our economy.

In a game, players spin a wheel with ten equally likely outcomes, 1-10. Find the probability that:

(a) In a single spin, the number that comes up is odd AND less than 5.

(b) In a single spin, the number that comes up is odd OR less than 5.

(c) In two spins, an odd number comes up first and a number less than 5 comes up second.

Michael Jordan likes to take 3-point shots. In fact, the number of 3-point shots he takes up to
time t is a Poisson process with rate 10 per hour. We assume that a game starts at 6pm.
(a) What is the expected number of 3-point shots he takes in the first 10 minutes of a game?
(b) What is the expected number of 3-point shots he takes between 6:20pm and 6:30pm?
(c) What is the probability that he takes exactly one 3-point shot between 6:20pm and 6:30pm?
(d) What is the expected time he takes 5 3-point shots?
(e) Suppose he didn't take any 3-point shot in the first 10 minutes. Given that he has not taken
any 3-point shot in the first 10 minutes, what is the expected time it takes for him to take
the first 3-point shot?
Now suppose that Michael can make any particular 3-point shot with probability 0.4
(independently of all other shots).
(f) What it the expected number of 3-point shots he makes in the first 30 minutes of a game?
(g) What is the probability that he makes exactly two 3-point shots in the first 20 minutes?
(h) What is the probability that he makes at least three 3-point shots in the first 30 minutes?
(i) What is the expected time it takes for him to successfully score his first 3-pointer?
(j) What is the probability that he attempts three 3-point shots in the first 15 minutes and only
one of the 3-point shots is successful?
(k) What is the probability that the first five 3-point shots are all successful?
Meanwhile, independently of his 3-point shots, Michael takes 2-point shots according to a
Poisson process, and the mean time between two successive 2-point shots is 3 minutes.
(l) What is the probability that he will take his first 2-point shot before his first 3-point shot?
(m) What is the expected amount of time until he takes his third shot (for either 2 or 3 points)?
Now suppose that Michael can make any particular 2-point shot with probability 0.6
(independently of all other shots).
(n) What is the mean and variance of the number of points (from either 2-point shots or 3-point
shots) he makes during the first 20 minutes of a game?