Question

In: Statistics and Probability

1. You are given Pr(A) = 0.3, Pr(B) = 0.5 and Pr(A ∪ B) = 0.6....

1. You are given Pr(A) = 0.3, Pr(B) = 0.5 and Pr(A ∪ B) = 0.6. (a) WhatisPr(A∩B)?

(b) What is Pr(notA)?

2. A bag contains 30 balls of the same size. Each ball is either red or green.

The probability of choosing a green ball is 0.7. How many of the balls are red?

3. Given nPr =42 and nCr =7 find the value of r?

4. We have Pr(A|B) = 0.3 and Pr(B) = 0.45. What is Pr(A ∩ B)?

5. How many 3 digit numbers can be created from the set {1, 2, 3, 4, 5, 6} if the digits cannot be repeated?

6. What is the probability of choosing 10 cards at random from a standard deck of 52 cards and getting exactly 2 queens?

7. What is the variance of the numbers 3, 7, and 8?

8. We have a discrete probability distribution where P r(X = 1) = 0.2,

Pr(X = 2) = 0.3 and Pr(X = 3) = 0.5. Determine μ.

9. We have a discrete probability distribution where P r(X = 1) = 0.6,

Pr(X=3)=0.1,Pr(X=5)=0.3andμ=2.4. Determineσ2.

10. We have a binomial distribution where the probability of success is 0.4 and the number of trials is 3,000. What is the variance of the distribution?

HELP 1-10!!!!!!!!

Expert Solution

orchestra answered 2 years ago

Given P(A) = 0.6, P(B) = 0.5, P(A | B) = 0.3, do the following. (a)...

Given P(A) = 0.6, P(B) = 0.5, P(A | B) = 0.3, do the following. (a) Compute P(A and B). (b) Compute P(A or B).

If A and B are mutually exclusive, with P(A) = 0.3, P(B) = 0.5. What is...

If A and B are mutually exclusive, with P(A) = 0.3, P(B) = 0.5. What is the probability that •either A or B occurs; •A occurs but B does not; •both A and B occur; •neither A nor B occur; •A or B but not both?

Sucrose (M) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Initial Weight (g) 6.25 6.33 6.38...

Sucrose (M) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Initial Weight (g) 6.25 6.33 6.38 6.50 6.54 6.40 6.56 6.25 Final Weight (g) 6.76 6.70 6.72 6.57 631 6.04 6.10 5.77 ∆ Weight (g) 0.51 0.37 0.34 0.07 -0.23 -0.36 -0.46 -0.48 %∆ Weight 0.08 0.06 0.05 0.01 -0.03 -0.05 -0.07 -0.08 a. Sucrose concentration at which zero percent change in weight is observed is: b. Determine the water potential (Ψw ) of the potato tissue. Show your calculations.

Alice solves every puzzle with probability 0.6, and Bob, with probability 0.5. They are given 7...

Alice solves every puzzle with probability 0.6, and Bob, with probability 0.5. They are given 7 puzzles and each chooses 5 out of the 7 puzzles randomly and solves them independently. A puzzle is considered solved if at least one of them solves it. What is the probability that all the 7 puzzles happen to be solved by at least one of them?

PROBABILITY 2. Given the following table x 0 1 2 3 Pr(X=x) 0.25 0.4 0.3 0.05...

PROBABILITY 2. Given the following table x 0 1 2 3 Pr(X=x) 0.25 0.4 0.3 0.05 answer each of the questions. Find µX and σX . Given that Y = -X+2 find µY and σY . 2B. Suppose that in the game of AFL the mean total number of points per match is 185 with a standard deviation of 33. Suppose that a season involves 202 matches. If the total points are normally distributed then answer the following questions....

Q1. Given the following Information Investment Expected return Standard deviation 1 0.12 0.3 2 0.15 0.5...

Q1. Given the following Information Investment Expected return Standard deviation 1 0.12 0.3 2 0.15 0.5 3 0.21 0.16 4 0.24 0.21 U=E(r) - (A/2)s2 , where A=4.0 a) Briefly describe the variable of E(r), s and A and how these variables affect the utility of individual. b) Based on the utility function above, which investment would you select? (shows your calculation. c) Redo part (b) if the investor is risk neutral.

Consider the following Markov chain: 0 1 2 3 0 0.3 0.5 0 0.2 1 0.5...

Consider the following Markov chain: 0 1 2 3 0 0.3 0.5 0 0.2 1 0.5 0.2 0.2 0.1 2 0.2 0.3 0.4 0.1 3 0.1 0.2 0.4 0.3 What is the probability that the first passage time from 2 to 1 is 3? What is the expected first passage time from 2 to 1? What is the expected first passage time from 2 to 2 (recurrence time for 2)? What is the relation between this expectation and the steady-state...

) In a market with three assets, the portfolios P1 = (0.6, 0.3, 0.1) and P2...

) In a market with three assets, the portfolios P1 = (0.6, 0.3, 0.1) and P2 = (- 0.2, 0.5, 0.7) lie on the Minimum Variance Set. The portfolios have returns 12% and 4% respectively. a) Find the portfolio on the MVS with return 14%. b) Does the portfolio P = (0.1, 0.4, 0.5) lie on the MVS ? Explain.

Mg standard Absorbance %RSD 0.5 0.09533 0.3 1 0.1209 0.2 2 0.17304 0.3 5 0.28137 0.2...

Mg standard Absorbance %RSD 0.5 0.09533 0.3 1 0.1209 0.2 2 0.17304 0.3 5 0.28137 0.2 10 0.56901 0.5 20 0.87153 0.3 5 mL Unk 0.14296 0.2 [1] Make a calibration curve using the absorbances for the samples from 0.5 – 20 ppm. Include the intercept (0,0) as a data point. [2] Is the calibration linear, i.e., does the analysis follow Beer’s law? To discuss linearity, examine both the trend of the data relative to the least squares line and...

1. Given P(A) = 0.3 and P(B) = 0.2, do the following. (For each answer, enter a...

1. Given P(A) = 0.3 and P(B) = 0.2, do the following. (For each answer, enter a number.) (a) If A and B are mutually exclusive events, compute P(A or B). (b) If P(A and B) = 0.3, compute P(A or B). 2. Given P(A) = 0.8 and P(B) = 0.4, do the following. (For each answer, enter a number.) (a) If A and B are independent events, compute P(A and B). (b) If P(A | B) = 0.1, compute P(A...