Name: Question 4. Let Y be a discrete random variable with ply) given in the table...
(5) Let Yi,...Y be independent random variables from a distribution with distribution function PlY Su)- Fu), and density function f(w). Now let Ya) be the minimum of all the observations. Show that the density function of Ya) is given by fm) (y) = n(1-F(v))"-1/(y) Hint: First write out the CDF, P(Ya) S y), then using independence of the observations put it in terms of the distribution function F(v), and then take the derivative to get the density.
between 0 and 4, x-UlO,4]. Another random variable, Y, is given Q1) Random variable as a function of g(x), Y X has uniform distribution g(x) where g(x)- 3-х, 2 x < 3. 0, otherwise. For parts a, b, and c, plotting the function y g(x) can be very useful. a-What is P(Y 0) [4 points] b-What is P(Y 1) 13 points] c-Derive and plot the cumulative distribution function (CDF) of Y, Frv). [10 points) d-What is probability distribution of Y,...
between 0 and 4, x-UlO,4]. Another random variable, Y, is given Q1) Random variable as a function of g(x), Y X has uniform distribution g(x) where g(x)- 3-х, 2 x < 3. 0, otherwise. For parts a, b, and c, plotting the function y g(x) can be very useful. a-What is P(Y 0) [4 points] b-What is P(Y 1) 13 points] c-Derive and plot the cumulative distribution function (CDF) of Y, Frv). [10 points) d-What is probability distribution of Y,...
5. Let X be a discrete random variable. The following table shows its possible values r and the associated probabilities P(X -f(x) 013 (a) Verify that f(x) is a probability mass function (b) Calculate P(X < 1), P(X < 1), and P(X < 0.5 or X > 2). (c) Find the cumulative distribution function of X ompute the mean and the variance of
math 4. Let X be a random variable with the following cumulative distribution function (CDF): y <0 F(y) (a) What's P(X 2)? b) What's P(X > 2)? c) What's P(0.5<X 2.5)? (d) What's P(X 1)? (e) Let q be a number such that F()-0.6. What's q?
Cumulative distribution function The probability distribution of a discrete random variable X is given below: Value x of X P(x-x) 0.24 0.11 -2 0.26 0.11 Let Fx be the cumulative distribution function of X. Compute the following: X 5 ? 18+ (-2) - Px (-4) = 0
2). Consider a discrete random variable X whose cumulative distribution function (CDF) is given by 0 if x < 0 0.2 if 0 < x < 1 Ex(x) = {0.5 if 1 < x < 2 0.9 if 2 < x <3 11 if x > 3 a)Give the probability mass function of X, explicitly. b) Compute P(2 < X < 3). c) Compute P(x > 2). d) Compute P(X21|XS 2).
1. Let X be a discrete random variable with a cumulative distribution function: a. Use this cdf to fin the limiting distribution of the random variable when with , as n increases. Use the fact b. What kind of random variable is for large value of n? We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imagep= We were unable to transcribe this imageWe were unable to transcribe this imageWe were...
Question 3: Let X be a continuous random variable with cumulative distribution function FX (x) = P (X ≤ x). Let Y = FX (x). Find the probability density function and the cumulative distribution function of Y . Question 3: Let X be a continuous random variable with cumulative distribution function FX(x) = P(X-x). Let Y = FX (x). Find the probability density function and the cumulative distribution function of Y
5. Let X be a discrete random variable. The following table shows its possible values associated probabilities P(X)( and the f(x) 2/8 3/8 2/8 1/8 (a) Verify that f(x) is a probability mass function. (b) Calculate P(X < 1), P(X 1), and P(X < 0.5 or X >2) (c) Find the cumulative distribution function of X. (d) Compute the mean and the variance of X.