Using the definition of expectation directly, show that if X has distribution bin(n, p), then: E(X²) = np(1-p+np).
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- Calculate the conditional expectation of Y when X = 2. E(YX2)Find the expectation and varience of X.A game is fair when each player's expectation equates to zero. If we are paid ten dollars each time the sum of two tossed dice is greater than four, what should we pay in return each time the sum does not exceed four to make the game fair?
- The lifespan X (years) of a species of pig has pdff (x) = 3x2e−x^3 , 0 < x < ∞.What is the probability that a pig will live at least 1 year? Given that it lives 1 year, what is the conditionalprobability that it will live for at least another year?In a college,there are 20 major subjects and 40 minor subjects,these are divided into 20 groups of 2 students each , such that all the ways of dividing them into group are equally likely . A = no of groups having 1 major subject and 1 minor subject Find the expectation E(X) of thesample AMike, a lumber wholesaler, is considering the purchase of a (railroad) car- load of varied dimensional lumber. He calculates that the probabilities of reselling the load for $10,000, $9000, and for $8000 are 0.22, 0.33, and 0.45 respectively. In order to ensure an expected profit of $3000, how much can Mike pay for the load
- what is the step by step basis taken to solve the following jump discontinuity?Consider a 20-year-old male. Suppose the survival rate is reduced. 2% per year. That means survival rate at age 21 is 98%, and that at age 22 is 96%, etc. a) According to the above assumption, what is his maximum age? b) Compute the probability that he can celebrate his 60th birthday. Using R to slove it.1. If there are n random variables such that each expectation exist then prove that E(X1+…….+Xn ) = E(X1)+……..+E(Xn). Assume discrete.
- Let X denote the number of empty bins when 60 balls are thrown independently into 30 bins. What is the expectation of X ?The United States Department of Agriculture (USDA) found that the proportion of young adults ages 20–39 who regularly skip eating breakfast is 0.2380.238. Suppose that Lance, a nutritionist, surveys the dietary habits of a random sample of size ?=500n=500 of young adults ages 20–39 in the United States. Apply the central limit theorem to find the probability that the number of individuals, ?,X, in Lance's sample who regularly skip breakfast is greater than 126126. You may find table of critical values helpful. Express the result as a decimal precise to three places. Then, Apply the central limit theorem for the binomial distribution to find the probability that the number of individuals in Lance's sample who regularly skip breakfast is less than 9898. Express the result as a decimal precise to three places.The United States Department of Agriculture (USDA) found that the proportion of young adults ages 20–39 who regularly skip eating breakfast is 0.2380.238. Suppose that Lance, a nutritionist, surveys the dietary habits of a random sample of size ?=500n=500 of young adults ages 20–39 in the United States. Apply the central limit theorem to find the probability that the number of individuals, ?,X, in Lance's sample who regularly skip breakfast is greater than 126126. You may find table of critical values helpful. Express the result as a decimal precise to three places.