Consider the given discrete probability distribution. Find P(X>3). 1 2 3 4 5 P(x) 0.1 0.2 0.2 0.3 0.2 X a. 0.2 b. 0.3 C. 0.5 d. 0.7
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- The joint probability distribution function of X and Y is given by: 1 2 3 1 0.05 0.06 0.10 X 2 0.13 0.21 0.30 a. Find the conditional distribution of Y given X = 1 b. Find the conditional distribution of X given Y = 2 5 0.02 0.03 0.10Suppose the following joint probability table for X and Y. Answer the questions. X 1 3 Total -1 0.02 0.03 0.04 0.09 Y 2.75 0.03 0.15 0.16 0.34 3 0.09 0.15 0.06 0.30 4.55 0.16 0.11 0.27 Total 0.14 0.49 0.37 1.00 What is Var(Y|X = 3) – the conditional variance of Y, given that X = 3? Answer:I. Which of the following are discrete probability distributions? (Yes or No) 1. 4 P(x) 0.10 0.20 0.25 0.40 0.05 2. 2. 3 4 5 P(x) 0.05 0.25 0.33 0.28 0,08 3. 3 4 5 P(x) 0.08 0.25 0.34 0.31 0.04 4. 2 3 4 5 P(x) 0.03 0.22 1.01 0.23 0.02 5. 1 2 3 4 P(x) 0,05 0.27 0.34 0,28 0.06 6. 3 4 5 P(x) 3 3 10 10 10 7. 3 4 P(x) 15 15 8. 3 4 5 P(x) 25 25 25 25 9. 3 4 P(x) 7. 1 10 10 20 20 10. 2. 3 4 5 P(x) 0.212 0.113 0,125 0.224 0.306
- Which of the following tables represents a valid discrete probability distribution? X P(X=x) X P(X=X) X P(X=x) X P(X=x) 5 0.51 1 0.23 0 10 15 0.03 0.03 3 0.03 1 0.33 0.15 3 0.24 5 0.15 2 0.27 20 0.39 7 9 0.17 0.19 3 0.19 25 30 0.15 0.01 12 11 0.02 4 5 1.01 0.06 6 9 15 18 0.22 0.23 0.12 -0.03 0.43Use the table for the probability distribution to find the condition probability of X = 1 given that Y = 1. The table for the probability distribution is given below. f(1|1) = Give your answer to one decimal place. 1 y 1 | 1/16 3/8 5/16 1/8 1/4 1/16Assume that 12 jurors are randomly selected from a population in which 80% of the people are Mexican-Americans. Refer to the probability distribution table below and find the indicated probabilities. xx P(x)P(x) 0 0+ 1 0+ 2 0+ 3 0.0001 4 0.0005 5 0.0033 6 0.0155 7 0.0532 8 0.1329 9 0.2362 10 0.2835 11 0.2062 12 0.0687 Find the probability of exactly 7 Mexican-Americans among 12 jurors. Round your answer to four decimal places.P(x=7)=P(x=7)= Find the probability of 7 or fewer Mexican-Americans among 12 jurors. Round your answer to four decimal places.P(x≤7)=P(x≤7)= Does 7 Mexican-Americans among 12 jurors suggest that the selection process discriminates against Mexican-Americans? no yes
- Find the mean of the given probability distribution. The random variable x is the number of houses sold by a realtor in a single month Houses Sold (x) Probability P(x) at the Sendsom's Real Estate office. 0.24 1 0.01 2 0.12 3 0.16 4 0.01 5 0.14 0.11 7 0.21 Ο Α. μ-3.35 Ο Β. μ-3.60 O C. μΕ 3.40 O D. µ= 3.50I. Which of the following are discrete probability distributions? (Yes or No) 1. 3 4 5 P(x) 0.10 0.20 0.25 0.40 0.05 2. 3 4 P(x) 0,05 0.25 0,33 0.28 0,08 3. 4 5 P(x) 0.08 0.25 0.34 0.31 0,04 4. 2 3 4 5 P(x) 0.03 0.22 1.01 0.23 0.02 5. 3 4 5 P(x) 0.05 0.27 0.34 0.28 0.06 6. 2 3 4 5 P(x) 1 3 3 10 10 10 7. 3. 4 P(x) 15 15 8. 2 4 5 6 P(x) 4. 25 25 25 25 9. 3 4 P(x) 1. 3. 20 20 1 10 10 10. 1 3 4 P(x) 0.212 0.113 0.125 0.224 0.306 -Let X represent the number of tires with low air pressure on a randomly chosen car. The probability distribution of X is as follows. x 0 1 2 3 4 Px 0.1 0.2 0.4 0.2 0.1 find p(1)
- 1. For every given probability distribution, solve for the expected value. a. 1 2 3 4 5 P(X) ? 0.29 0.31 0.26 0.13 b. 3 9 12 15 P(X) 0.04 0.12 0.36 0.29 ? 2 8 10 P(X) 0.15 ? 0.29 0.21 0.12 d. X 4 10 P(X) k 0.24 2k 0.19 0.15 00 00 6. 4.Calculate the expected value for this discrete probability distribution: X P(x) 2 0.10 3 0.25 4 0.25 5 0.40 Write you solution to two decimal places.