1. The range of a random variable is {0, 1, 2, 3, x}, where x is unknown.If each value is equally likely and E = 6, determine x.2. A random variable has a distribution-XXx > 0x < 0ƒ€ (x) = {(1)0Find the maximum likelihood estimation of the unknown parameter ahaving the observations X₁,..., Xn.3. Let is a uniformly distributed random variable U(0, 1). Find thedistribution of a random variable n = −ln(1 - §).—4. The expected value Eg of a random variable & EN(u, 1) is a negativevalue. Prove that P(§ > 0) < 0.5

It is given that ξ is a random variable with values {0,1,2,3,x} with equal probability. Then the…

Answered: 1. The range of a random variable & is…

A First Course in Probability (10th Edition)

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Author:Sheldon Ross

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Chapter1: Combinatorial Analysis

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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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An ordinary (fair) coin is tossed 3 times. Outcomes are thus triples of "heads" (h) and "tails" (1) which we write hth, ttt, etc. For each outcome, let N be the random variable counting the number of heads in each outcome. For example, if the outcome is htt, then N (htt) = 1. Suppose that the random variable X is defined in terms of N as follows: X=2N-N2 -4, The values of X are given in the table below. Outcome hht tth hth thh tht ttt hhh htt Value of x -4 -3 -4 -4 -3 -4 -7 -3 Calculate the probabilities P(X=*) of the probability distribution of X. First, fill in the first row with the values of X. Then fill in the appropriate probabilities in the second row. Value of x _ _ _ p(X=x) _ _ _
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An ordinary (fair) coin is tossed 3 times. Outcomes are thus triples of "heads" (h) and "tails" (t) which we write hth, ttt, etc. For each outcome, let N be the random variable counting the number of heads in each outcome. For example, if the outcome is thh, then N (thh)=2. Suppose that the random variable X is defined in terms of N as follows: X=2N²-6N-4. The values of X are given in the table below. ttt hhh hth hht tht htt thh tth Value of X -4 -4 -8-8-8-8-8-8 Outcome Calculate the probabilities P (X=x) of the probability distribution of X. First, fill in the first row with the values of X. Then fill in the appropriate probabilities in the second row. Value x of X P(X=x) 7 00 X S
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1. The range of a random variable & is {0, 1, 2, 3, x)}, where x is unknown. If each value is equally likely and E = 6, determine x.