Consider the following probability density function f(x): f (x) 1 1 e* for 0 < a < 2 -2 e (a) Find the cumulative distribution function of X. In other words, what is F(x)? (b) Find the mean of X. (c) Find P(X> 1).
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A: Thanks for the question :)And your upvote will be really appreciable ;) Option A is correct
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- x- 5 for 5IfX has the probability density f(#) <1 Find F(x). Select one: O a F(2) = 1- O b. F(r) = 1 - Oc F(e) = = c. F() O d. F()=For what value of c is the function f(x) = {c/x³ if x ≥ 1 {gx3 otherwise a probability density function?Consider the following function:Consider the following exponential probability density function. 1 -x/4 f(x) = -e (a) Write the formula for P(x ≤ xo). for x ≥ 0 (b) Find P(x ≤ 2). (Round your answer to four decimal places.) (c) Find P(x ≥ 4). (Round your answer to four decimal places.) 0.3679 (d) Find P(x ≤ 5). (Round your answer to four decimal places.) (e) Find P(2 ≤ x ≤ 5). (Round your answer to four decimal places.)The exponential distribution is a probability distribution for non-negative real numbers. It is often used to model waiting or survival times. The version that we will look at has a probability density function of the form p(y|v) = exp(-e¯ºy — v) (1) where y R+, i.e., y can take on the values of non-negative real numbers. In this form it has one parameter: a log-scale parameter v. If a random variable follows an exponential distribution with log-scale v we say that Y~ Exp(v). If Y~ Exp(v), then E [Y] =e" and V [Y] = e²v. 1. Produce a plot of the exponential probability density function (1) for the values y E (0, 10), for v = 1, v = 0.5 and v= 2. Ensure the graph is readable, the axis are labeled appropriately and a legend is included. ta il 2. Imagine we are given a sample of n observations y = (y₁,..., yn). Write down the joint proba- bility of this sample of data, under the assumption that it came from an exponential distribution with log-scale parameter v (i.e., write down the…Q2. The probability density function of X is as follows. f(x) = 2 - 2x, for x = [0, 1] Which one of the following expressions can be used to find P(0.5 < X < 1.5)? F(x) is the cumulative distribution function of X. (A) 1 - F(0.5) (C) F (1.5)-f(0.5) (B) f(1.5)-f(0.5) (D) 1.5 (2 - 2x) dx (E) otherThe continuous random variable X has the following probability density function (pdf), for some positive constant c, for 0 < x < c. 3 (1+x)³ f(x)= (a). Prove that c= √3-1. (a) Accept c = √√3-1. Plot f(x) in the range. (b) Find E(X); Var (X) using numerical integration. (c) Use Inversion method, find 20 random numbers from X =Consider the following exponential probability density function. f(x) 1 -e ,-x/3 = for x > 0 (a) Write the formula for P(x 3). (Round your answer to four decimal places.) (d) Find P(x < 5). (Round your answer to four decimal places.) (e) Find P(2Consider the following constant function: f(x) = 3/4 If this function represents a probability density function, which of the following can be a set of realized values? A. 2/3 ≤ x ≤ 2 B. 1/4 ≤ x ≤ 1 C. 3 ≤ x ≤ 4 D. 1/2 ≤ x ≤ 3/2[1] The probability density function of a random variable X is SC(x + 4), -4 4.Consider the probability distribution function (PDF) f(r) = Ax sin r, for 0Recommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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