The expected value of discrete random variable is .
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The third choice is correct.
The payoff (X) for a lottery game has the following probability distribution. Find the expected value...
The table defines a discrete probability distribution. Find the expected value of the distribution. x 7 8 9 10 Pr(x) 1/3 1/3 1/3 0
Suppose you are facing a lottery that has a payoff of 10b pounds with probability 0.01 and that of 0 with probability 0.99. You are an expected utility maximiser with a utility function,u(x) = −exp(−ax) where x is the payoff in money terms and a > 0 is a parameter. What is the risk premium for this lottery - describe the risk premium as a function of ‘a’ and ‘b’.
The lottery commission has designed a new instant lottery game. Players pay $1.00 to scratch a ticket, where the prize won, X, (measured in $) has the following discrete probability distribution: P(X) 0.95 0.049 0.001 Which of the following best describes the standard deviation of X? Select one: o a. 14.552 in $2 ob. 3.815 in s O c.0.348 in $
2. (10 points) The random variable X has the following probability distribution x 2 3 5 8 Pr(X = x) 0.2 0.4 0.3 0.1 a) Pr (X<=3) P(X<=3) b) Pr( 2.7<X<5.1) c)Pr(X>2.5) d) E(X)
For a multistate lottery, the following probability distribution represents the cash prizes of the lottery with their corresponding probabilities. Complete parts (a) through (c) below. X (cash prize, $) Grand prize 200,000 10,000 100 P(x) 0.00000000877 0.00000023 0.000001734 0.000147996 0.004260186 0.008970789 .01261213 0.97400692623 4 3 0 0 (a) If the grand prize is $13,000,000, find and interpret the expected cash prize. If a ticket costs $1, what is your expected profit from one ticket? The expected cash prize is $...
Given a lottery P, let E (P) be the expected value of the lottery P. For example, if P = ($10, 0.5; $0, 0.5), then E (P) = 0.5 × 10 + 0.5 × 0 = 5 (1) Ann has vNM utility u1 (x) = x, Bob has utility u2 (x) = √ x and Carl has utility u3 (x) = x^3 . Who is risk neutral, risk averse and risk loving? (2) Consider the lottery P again. Find the...
The humidity level, X, in Tropicana Field in Tampa at the time of a night game ranges from 40% to 100 %. (.40 to 1.00) The random variable X has cumulative distribution F with the following definition: F(x) 0 for x < 40, F(x)= 5(X-.4)(2-x) for .4 s x 1.0, F(x)=1 for x 2 1.0. a) What is the probability density function for X for .4 s xs 1.0? 1-5(x-4)(2-x) 5(2-x)+5(x-0.4) 5(2-x)-5(x-0.4) Odnorm(x,2,.4 b) What is the probability that X>0.5?...
(2.) A discrete-tim e Markov chan X, E {0,1,2) has the following transition probability matrix: 0.1 0.2 0.7 P-10.8 0.2 0 0.1 0.8 0.1 Suppose Pr(Xo = 0) = 0.3, Pr(X,-1) = 0.4, and Pr(Xo = 2) = 0.3. Compute the following. .lrn( (a) Pr (X0-0, X,-2, X2-1). (b) Pr(X2-iXoj) for all i,j
2.1 Let X be a discrete random variable with the following probability distribution Xi 0 2 4 6 7 P(X = xi) 0.15 0.2 0.1 0.25 0.3 a) find P(X = 2 given that X < 5) b) if Y = (2 - X)2 , i. Construct the probability distribution of Y. ii. Find the expected value of Y iii. Find the variance of Y
An instant lottery game gives you probability 0.10 of winning on any one play. Plays are independent of each other. You play 4 times. a) If X is the number of times you win, contract the probability distribution of X. b) What is the probability that you don't win at all? c) What is the probability that you win at least once? d) What is the expected value of X? What is the standard deviation of X?