Mean, Variance, and Standard Deviation of a Discrete Random Variables

Solve the following problems. 1. Let X represent the number of times Norman visits an Internet Cafe to play video games in a one-week period. The probability distribution of X is shown below. X 0 2 3 4 P(x) 0.06 0.18 0.40 0.28 0.08 Find the expected value and variance of X. 2. A researcher surveyed the households in a remote area. The random variable X represents the number of high school graduates in the households. The probability distribution of X is shown below. X 0 2 3 0.02 0.18 0.40 0.10 P(x) 0.30 Find the expected value and variance of X. I gninnale mit dull'D sonsi 2 and to arpaio andT 3. The random variable x represents the number of taxi cabs a doctor meets on his way to the hospital. The probability distribution of X is given in the following distribution table. X 0 1 13 4 5 P(x) 0.01 0.15 10.20 0.25 0.30 0.09 Find the expected value and variance of X.wooo bsaniday as paraat unveil 4 The following are the results of a study of the number of defective oven toasters produced by a certain company. Use the data and the associated probabilities to compute the expected number of defective oven toasters. intion thi X 0 1 2 3 P(x) 4 0.08 5 0.16 0.28 0.27 0.15 0.06 5. The weekly demands for mobile phones in certain store are shown below together with the associated probabilities Demand 1 Probability 2 3 0.15 4 0.35 0.40 0.10 Determine the expected demand for mobile phones.Find the variance and the standard deviation of each of the following probability distributions. X 0 1 2 3 4 15 P(x) 0. 123 0. 134 0.211 0.3218 0.140 0.071\fSolve the following problems. 1. The officers of the Science Club are planning to sell 125 tick to be raffled during the school's foundation day. One ticket will win P2,000 and the other tickets will win nothing. If you will buy one ticket, what will be your expected gain? Determine the expected demand for mobile phones. 2. A lottery will be conducted for the benefit of the poor but deserving students of a certain school. Four hundred tickers will be sold. One ticket will win P2,000 and the other tickets will win nothing. If you will buy one ticket, what will be your expected gain? 3. Laverny tosses an unbiased coin. He receives P100 if a head pays P40 if a tail appears. Find the expected and the variance of his gain. 4. Five hundred tickets will be sold and these will be raffled during the town fiesta. One of these tickets will win P3,000 and the rest will win nothing. What will be the expected outcome and variance of your gain if you will buy one of the tickets? 5. Dan tosses an unbiased coin. On each toss, he wins P50 if a appears, expected value and variance of his gain? and loses P40 if a tail appears. What will be the