please, solve 4 question D1.Find the expected value and variance of the discrete random variable Xwith the following PDF:x = 14'P(X = x) =X = 23-D2.If E(X) = 10 and Var(X) = 2, find Var(2 – 5X).-D3.Let X be a random variable with the probability density function f(x),5x4,0,f(x) = { 32**, 0

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Description: please, solve 4 question D1.Find the expected value and variance of the discrete random variable Xwith the following PDF:x = 14'P(X = x) =X = 23-D2.If E(X) = 10 and Var(X) = 2, find Var(2 – 5X).-D3.Let X be a random variable with the probability dens

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Math

Probability

expected value and variance

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter6: Exponential And Logarithmic Functions

Section6.8: Fitting Exponential Models To Data

Problem 56SE: Recall that the general form of a logistic equation for a population is given by P(t)=c1+aebt , such...

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Recall that the general form of a logistic equation for a population is given by P(t)=c1+aebt , such that the initial population at time t=0 is P(0)=P0. Show algebraically that cP(t)P(t)=cP0P0ebt .
For a certain psychiatric clinic suppose that the random variable X represents the total time (in minutes) that a typical patient spends in this clinic during a typical visit (where this total time is the sum of the waiting time and the treatment time), and that the random variable Y represents the waiting time (in minutes) that a typical patient spends in the waiting room before starting treatment with a psychiatrist. Further, suppose that X and Y can be assumed to follow the bivariate density function fXY(x,y)=λ2e−λx, 0<y<x, where λ > 0 is a known parameter value. (a) Find the marginal density fX(x) for the total amount of time spent at the clinic. (b) Find the conditional density for waiting time, given the total time. (c) Find P (Y > 20 | X = x), the probability a patient waits more than 20 minutes if their total clinic visit is x minutes. (Hint: you will need to consider two cases, if x < 20 and if x ≥ 20.)
Let X denote 0.025 × the ambient air temperature (˚C) and let Y denote the time (min) that it takes for a diesel engine to warm up. Assume that (X, Y) has joint probability density function. f(x,y) = 1.6x (1 − x)(6 + 5x − 4y), for 0 < x < 1, 0 < y < 0.5. What is the probability that the air temperature will be less than 20˚C (so X ≤ 0.5) and it will take no more than 0.2 minute for the engine to warm up?
2. Identify the probability density function, then find the mean and variance without integrating. b. f(x) =1/6 e^−x/6, [0,∞) c. f(x) =1 / 3√2π e^−(x−16)^2/18, (−∞,∞)
Let X denote 0.025 × the ambient air temperature (˚C) and let Y denote the time (min) that it takes for a diesel engine to warm up. Assume that (X, Y) has joint probability density function f(x,y) = 1.6x (1 − x)(6 + 5x − 4y), for 0 < x < 1, 0 < y < 0.5. While you cannot guess the value of the correlation from the regression curve for X or Y, do they suggest whether it likely is positive or negative?
Q4) If X is a continuous random variable having pdf ke~ (2x+3y) x>0y>0 xy) = = e p(x) { 0 otherwise Find a) the constant k b) P(X>1) ¢) X, X2, 02, standard deviation.
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Let X denote 0.025 × the ambient air temperature (˚C) and let Y denote the time (min) that it takes for a diesel engine to warm up. Assume that (X, Y) has joint probability density function f(x,y) = 1.6x (1 − x)(6 + 5x − 4y), for 0 < x < 1, 0 < y < 0.5. Find the conditional pdf of Y, given X = x. Compare this to the marginal pdf of Y. Are air temperature and engine warm-up time independent?
Let X denote 0.025 × the ambient air temperature (˚C) and let Y denote the time (min) that it takes for a diesel engine to warm up. Assume that (X, Y) has joint probability density function f(x,y) = cx (1 − x)(6 + 5x − 4y), for 0 < x < 1, 0 < y < 0.5. Find the conditional pdf of Y, given X = x. Compare this to the marginal pdf of Y. Are air temperature and engine warm-up time independent?
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