last item only (letter d) The current in a certain circuit as measured by an ammeter is a continuous random variable X with the following density function.[0.075x+0.2 3≤x≤50otherwise(a) Graph the pdf.0.60.50.40.30.2f(x) =f(x)0.1O2(b) Calculate P(X ≤ 4).0.46250.075x + 0.2 dx= 0.075 5+ -0.2x= 1.9375 -=13Verify that the total area under the density curve is indeed 1.65⁰.(c) Calculate P(3.5 ≤ x ≤ 4.5).0.5Calculate P(4.5 < X).0.278140.9375How does this probability compare to P(X < 4)?OP(X ≤ 4) < P(X < 4)ⒸP(X ≤ 4) = P(X < 4)OP(X ≤ 4) > P(X < 4)f(x)0.60.50.40.30.20.112345Xf(x)0.60.50.40.30.20.1O12345f(x)0.60.50.40.30.20.1xo12345X

As per given instructions i have to slove part (d) only

Answered: The current in a certain circuit as…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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The current in a certain circuit as measured by an ammeter is a continuous random variable X with the following density function: f(x ) = { .075x + .2 3< x < 5 0 otherwise a. Graph the pdf and verify that the total area under the density curve is indeed b. Calculate P(X < 4). How does this probability compare to P(X <4)? c. Calculate .P(3.5< X< 4.5) and also .P(4.5 < X).
The current in a certain circuit as measured by an ammeter is a continuous random variable X with the following density function. What is P(X ≤ 4)? What is P(4.5 < X)?
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.)
On a production line, parts are produced with a certain average size, but the exact size of each part varies due to the imprecision of the production process. Suppose that the difference between the size of the pieces produced (in millimeters) and the average size, which we will call production error, can be modeled as a continuous random variable X with a probability density function given by f(x) = 2, 5e^(-5|x|), for x E R (is in the image). Parts where the production error is less than -0.46 mm or greater than 0.46 mm should be discarded. Calculate (approximating to 4 decimal places): a) What is the proportion of parts that the company discards in its production process? b) What is the proportion of parts produced where the production error is positive? c) Knowing that for a given part the production error is positive, what is the probability of this part being discarded?
Let Y1 = 0.5, Y2 = 0.25, Y3 = 0.75, Y4 = 0.25 and Y5 = 1.25 be a random sample of width 5 selected from the population with the following probability density function. Which of the following is the estimation value obtained by the moment method for the unknown q parameter of this population?
The PDF of a continuous random variable X is as follows: f(X)= c(4x2 - 2x2) 0<* x <* 2 (*less or equal to) a. For this to be a proper density function, what must be the value of c ?
A continuous random variable has a density function f(x)= 2(5-x)/5 , where 2<x<3. Calculatethe following probability correct up to 3 decimal places, and make the graph for part (a) only in Answer sheet:P (x < 2.5)P (x > 2.2)P (2.1 ≤
A continuous random variable has a density function f (X)=2(5-x)/5 , where 2<x<3. Calculate the following probability correct up to 3 decimal places, and make the graph for part (a) only in Answer sheet: P (x < 2.5) P (x > 2.2) P (2.1 ≤ ? ≤ 2.7)
Suppose that X, Y are jointly continuous with joint probability density function f( x, y){ xe^-x(1+y), ifx >0 and y >00, otherwise. (a) Find the marginal density functions of X and Y. (b) Calculate the expectation E[XY]. (c) Calculate the expectation EIX/(1+ Y )1. (e) Determine if the random variables X and Y in this exercise are independent.
An insurance company finds that the proportion X of itssalespeople who sell more than $25,000 worth of insurance in a given week is a random variable with the beta probability density functionf(x) = 60x^3(1 - x)^2, 0 ≤ x ≤ 1.(a) Compute E(X ) and give an interpretation of thisquantity.(b) Compute Var(X ).
Suppose that X is a continuous random variable with density function f(x). If f(x)=k for −5≤x≤3 and f(x)=0 otherwise, determine the value of k.
Let Y be a random variable whose density function is 3y2 ? y3? f(y|θ)= θ3 exp −θ3 , y>0,where θ > 0 is a parameter. Using an appropriate pivotal quantity, verify that?Y,Y? (− log α)1/3 (− log(1 − α))1/3is a confidence interval for θ with coverage probability 1 − 2α.

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