Please help with #194 a and b
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Please help with #194 a and b Thank you :) 194. Suppose that X has a...
1. Suppose that X is continuous random variable with PDF f(x) and CDF F(x). (a) Prove that if f(x) > 0 only on a single (possible infinite) interval of the real numbers then F(x) is a strictly increasing function of x over that interval. [Hint: Try proof by contradiction]. (b) Under the conditions described in part (a), find and identify the distribution of Y = F(x). 2. Suppose now that X ~ Uniform(0, 1). For each of the distributions listed...
Suppose that X has CDF Exercise 24.22. Suppose that X has CDF 0 If x < 0, İf 0 < x < 1, İf 1 < x < 7, a. Find the density fx(a) b. Find the median of X
please show work and explain for my understanding. Suppose that the continuous random variable X has pdf given by: x <1 0.16x 15 x 33 f(x)= 0.06 3<x55 [124 x>5 • Find the corresponding cdf for X: You must determine the arbitrary constants. x <1 1<x3 Ex(x)={ 3< x <5 x>5 • Use the cdf to find P(2.4 <x< 10) = • Use the cdf to determine the following percentiles: the 50th percentile (median) the 80th percentile the 90th percentile
Simple Probability Question, Please explain with details, thank you so much. Suppose that the cumulative distribution function of the discrete random variable X is given by x V < 0 1L F(x) = { 1 +71 051 x < 2 1 VI Find P{X = 1}, P{X = 2}, P{X = 3} o 1, 11,1 OZ, ÉS 0 ];j; oh, o 12 Find P (} < X < ;) оооо Consider the following two functions S c(2x – 2y) 0...
6. Suppose that K is a positive constant and f(x) = K sin x is a pdf on 0 < x <T. (a) Find K. (b) Find the cumulative distribution function (cdf) off. (c) Find the inverse cdf off.
Please can someone help me with this exercise? Thank you. e bounded on a nondegenerate interval [a, b]. Prove that f is e 0 there is a partition Pe of 5.1.10. Let f b integrable on [a, b] if and only if given la, b] such that P Po implies IU (f, P)-L(f, P)I < ε.
СТ 5. The triangular distribution has pdf 0<<1 f(x) = (2-2) 1<x<2. It is the sum of two independent uniform(0.1) random variables. (a) Find c so that f(x) is a density function. (b) Draw the pdf, and derive the cdf using simple geometry. (c) Derive the cdf from its definition. (d) Derive the mean and variance of a random variable with this distribution.
need help please and thank you A) Find the cdf (c) corpute CLA and Exercise 3.24. Suppose X has a discrete distribution with probability mass function given by I x 1 2 3 | px(x) 1/ 72/74/7|
Please show the steps and the answers Suppose (X, Y) takes values on the unit square [0, 1] x [0, 1) with joint pdf f(x,y)- 3. (x2 + Y2). a) Find the marginal probability density function fx(x) and use it to find P(X < 0.5). b) Find the joint distribution function.
2. A random variable X has a cdf given by F(x) = 1 . x < 0 0 < x < 1 <3 x > 3 11, (f) What is P(X = 1)? (g) Find E(X), the expectation of X. (h) Find the 75th percentile of the distribution. Namely, find the value of 70.75 SO that P(X < 70.75) = F(710.75) = 0.75. (i) Find the conditional probability P(X > X|X > 3).