A discrete random variable, y, has a probability distribution y: 6, 7, 8,9, 10,11 nd P :0.13,0.26 ,0.14, 0.09 ,0.11,0.27 Calculate the standard deviation of y. a. 0 O O b. 1 C. 0.54 no one of them O
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- The monthly return of a particular stock follows the normal distribution with mean 0.01 and standard deviation 0.14. Find the probability that the monthly return of the stock will be less than 0.16. Select one: a. 0.6554 b. 0.6423 c. 0.1423 d. 0.8577 e. 0.3577Assume X has the following probability distribution: X 1 2 3 4 P(X) .1 .5 .2 .2 Compute the standard deviation of X.Let X be a random variable that has a Poisson distribution. If the probability that X is greater than 0 is 0.9967. Then the mean, variance, and the standard deviation of the probability distribution of X are, respectively, (Choose one from the following which is closest to the correct answer) O c. 4.3, 2.5, 1.6. O a. 5.7, 5.7, 2.4. O d. 5.7, 2.5, 6.0. O b. 5.5, 2.5, 1.6. O e. 10.0, 4.3, 1.6.
- Let x be a random variable with the following probability distribution 2 5 P(x) 0.3 0.2 0.3 k 0.1 Find the expected value and the standard deviation for x. Select one: O a. 2.7 and 2.1 O b. 2.5 and 3.2 O c. 2.7 and 3.2 O d. 2.8 and 2.1Assume z is a standard normal random variable. Then P(z ≥ 2.48) equals _____. a. 0.4934 b. 0.50 c. 0.0066 d. 0.9934Let X be a random variable with the following probability distribution: - 4 3 5 f(x) 0.6 0.3 0.1 Find the standard deviation of X. The standard deviation is . (Round to two decimal places as needed.)
- The joint probability distribution of the random variables X and Y is given below: ? (?, ?) = ???, 0 <? <2, 0 <? <? 0, other a. Find the value of the constant. b. Calculate and interpret the covariance and correlation of the X and Y random variables. c. Calculate the expected value and variance of the random variable ? = 2? − 3? + 2.The probability distribution of random variable X is defined as follows: X 0 1 2 3 4 Probability 0 0.3 0.1 0.3 0.3 Find the expected value and the standard deviation of X.Suppose a discrete random variable X takes only three values 0, 2 and 3. If P(0)=0.5, P(2)=0.2 and P(3)=D0.3 then P(X>1) is equal to: Select one: a. 0.3 b. 0.2 C. 0.5 d. 0
- Let x be a random variable with the following probability distribution 2 4 8 10 P(x) k 0.15 4k 0.1 0.25 Find the expected value and the standard deviation for x. Select one: a. 7 and 1.24 O b. 6.5 and 2.519 C. 6.5 and 2.414 O d. 10.5 and 2.519High school students in Michigan sometimes get "snow days" in the winter when the roads are so bad that school is canceled for the day. Define the random variableX = the number of snow days at a certain high school in Michigan for a randomly selected school year. Suppose the table below gives the probability distribution of X. 1. Value x, 1. 3 4 5 6 7 8 9 10 Probability p, ? 0.19 0.14 0.10 0.07 0.05 0.04 0.04 0.02 0.01 0.01 (a) Write the event “the school year has O snow days" in terms of X. Then find its probability. (b) At this high school, if more than 5 snow days are used over the course of the year, students are required to make up the time at the end of the school year. What's the probability that a randomly selected school year will require make-up days?The monthly return of a particular stock follows the normal distribution with mean 0.01 and standard deviation 0.14. Find the probability that the monthly return of the stock will be between -0.02 and 0.05. Select one: O a. 0.9691 O b.0.5309 O C.0.1973 d. 0.8027 e. 0.0309