Expectation and variance of a random variable Let X be a random variable with the following probability distribution. Value x of X P(X=x) 40 0.30 50 0.10 60 0.20 70 0.15 80 0.25 Complete the following. (If necessary, consult a list of formulas.) (a) Find the expectation E (X) of X. E(x) -0 (b) Find the variance Var(X) of X. Var(x) – I Explanation Check

Random Variable X Directions: Compute the expected value, variance, and standard deviation for random variable X whose probability table is given below: Possible Outcome 8 10 12 14 0.1 0.4 0.4 0.1 Probability Probability Table for X 1. The Expected Value of X is E(X) 2. The Variance of X is Var(X) 3. The Standard Deviation of X is Std(X) Random Variable Y Directions: Compute the expected value, variance, and standard deviation for random variable Y whose probability table is given below: Possible Outcome 8 10 12 14 Probability 0.3 0.2 0.2 0.3 Probability Table for Y 1. The Expected Value of Y is E(Y) 2. The Variance of Y is Var(Y) 3. The Standard Deviation of Y is Std(Y)

Given the random variable X and its probability density function​ below, find the​ mean, variance, and standard deviation of X.   X ​Pr(X) 0 0.3 3 0.7     Mean​ =   Variance​ =   Standard Deviation​ =

Find the probability that X=2. Find the expected value.

Directions: Compute the expected value, variance, and standard deviation for random variable X whose probability table is given below: Possible Outcome -1 0 1/7 1/7 Probability Probability Table for X 1. The Expected Value of X is E(X) 2. The Variance of X is Var(X) 3. The Standard Deviation of X is Std(X) 1 2 5/14 5/14

P(x) 0.091 A sociologist randomly selects single adults for different groups of three, and the random variable x is the number in the group who say that the most fun way to flirt is in person. 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. 0.332 0.418 3 0.159 ..... Does the table show a probability distribution? Select all that apply. O A. Yes, the table shows a probability distribution. B. No, the sum of all the probabilities is not equal to 1. C. No, the random variable x is categorical instead of numerical. O D. No, not every probability is between 0 and 1 inclusive. E. No, the random variable x's number values are not associated with probabilities. Find the mean of the random variable x. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. µ= adult(s)…