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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’.
A lottery ticket costs $2 and has a random 5-digit number. The payoff depends on the largest number of repeated digits. There is no prize if no digit is repeated. The prize is $2 if some digit is repeated exactly twice, $5 if a digit is repeated exactly 3 times, $10 if a digit is repeated exactly 4 times, and $1000 if a digit is repeated exactly 5 times. Let X be the net earning in playing the game. a)...
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