Additional Problem 5. Suppose that X is equally likely to take any of the values 1,...
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» Additional Problem 4. We say that mp is the pth quantile of the distribution function F if Find m, for the distribution having the following density functions: (a) f(z) = 5e-5e, X 〉 0 (b) f(z) = 3, 0 〈 x 〈 2. (c) f(x) =ー2ー r+1 ,一1 < x 〈 1. Answers: (a) -r In (1-p), (b) 2p1/4, (c)-1 +2, P » Additional Problem 5. Suppose that X is equally likely to take any of...
Suppose three dice are rolled. Each die is equally likely to take values between 1 and 6, inclusive. Given that all three dice have different values. Find the probability that the smallest value of the three dice is 2.
X, be equally likely to be any of the n! permutations of 72. Let X1, . . , (1, 2, . ,n) Argue that
1. Suppose that each child born to a couple is equally likely to be a boy or a girl, inde- pendently of the gender distribution of the other children in the family. For a couple having 5 children, compute the probabilities of the following events: (a) All children are of the same gender (b) The 3 eldest are boys and the others girls. (c) Exactly 3 are boys. (d) The 2 oldest are girls. e) There is at least 1...
Problem 6 (15 pts) Suppose we roll a die that is equally likely to have any of its 6 sides appear face up. Find ElX), where X is the side facing up.
Problem 1. Suppose X is N(12,42) i) what range of values does X take on 68% of the time? ii) what range of values does X take on 95% of the time? Let Y be the sum of three random variables described above. ii) What is the distribution of Y? iv) U is N(10,4) and V is N(8,9). What is the distribution of U-V?
Problem 1. Suppose X is N(12,42) i) what range of values does X take on 68%...
if you can answer any of these i’d would appreciate it
greatly
1. List the reasons why the expectation and the variance are used as measures of the center and the spread of a probability distribution. 2. The random variable Z in Table 8.4 takes the values 3000 and 4000 with probability of 0.5. Compute MAD(2) and StDev(z). State in words why MAD(Z) and StDev(2) take the values that they do. 3. As an alternative to the expectation, one could...
Let XXn Be equally likely to be any of the n! permutations of (1, 2,., ).,Argue that 7 jx, 2 m(n + 1)2
Let XXn Be equally likely to be any of the n! permutations of (1, 2,., ).,Argue that 7 jx, 2 m(n + 1)2
1. Suppose that X and Y are random variables that can only take values in the intervals 0 X 2 and 0 Y 3 2. Suppose also that the joint cumulative distribution function (cdf) of X and Y, for 0 < 2 and 03 y 3 2, is as follows: Fy). 16 [5] (a) Determine the marginal cdf Fx(x) of X and the marginal cdf Fy () of Y [5] (b) Determine the joint probability density function (pdf) f(x, y)...
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Suppose that X is a uniform random variable on the interval (0, 1) and let Y = 1/X. a. Give the smallest interval in which Y is guaranteed to be. Enter -Inf or Inf for – or o. Interval:( b. Compute the probability density function of Y on this interval. fy(y) = Suppose that X ~ Bin(4, 1/3). Find the probability mass function of Y = (X – 2)2. a. List all possible values that...