An electronic system has one each of two different types of components in joint oper-ation. Let Y₁ and Y₂ denote the random lengths of life, in hundreds of hours, of thecomponents of type I and type II, respectively. The joint density function is given by:f(y₁, y2)=[(1/8)y₁e¯(v₁+y²)/²_if y₁ > 0, y2 > 0elsewhere0(a) Verify that f(y₁, y2) is a probability density function.(b) Find P(Y₁ > 1, Y2₂ > 1).(c) Find the probability that a component of type II will have a life length in excessof 200 hours.(d) Is fy₁,Y₂ (y₁, y2) = fy₁ (₁) fy₂ (Y2)?(e) One way to measure the relative efficiency of the two components is to computethe ratio Y₂/Y₁. Find E(Y₂/Y₁).

According to guidlines we are supposed to solve first three subparts only and rest can be…

Answered: An electronic system has one each of…

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter13: Probability And Calculus

Section13.CR: Chapter 13 Review

Problem 29CR

See similar textbooks

Similar questions

Let Y and Y, be two independent exponential random variables, both with mean B > 0. Find the density function of Y +Y2.
Exercise 20. Let X1 and X2 be iid U(0,1) random variables. Find the joint probability density function of Y1 = X1+ X2 and Y2 = X2 – X1.
A student has 3 volumes of short stories and 2 novels on a bookshelf. She selects 3 books at random to take home over vacation. A random variable X is defined to be the number of novels selected. Find the values assumed by X and its density function.
The life lengths of two transistors in an electronic circuit is a random vector (X; Y) where X is the life length of transistor 1 and Y is the life length of transistor 2. The joint probability density function of (X; Y) is given by x 2 0, y 2 0 fx.,fx.v) = 20 else Then the probability that the first transistor burned during half hour given that the second one lasts at least half hour equals Select one: a. 0.606 b. 0.3935 C. 0.6318 d. 0.3669 e. 0.7772
Show that if a random variable has a uniform density with parameters α and β, the probability that it will take on a value less than α+p(β-α) is equal to p.
Let X and Y be independent Gaussian random variables, each distributed according to (0, σ2). 1. Find the joint density function of the random variables Z = X + Y and W = 2X −Y . What is the correlation coefficient between these two random variables
Let x be a continuous random variable with the density function: f(x) = 3e-3x when x>0 and 0 else Find the variance of the random variable x.
Asap
The density function of a random variable is given as fx(x) = ae bx x20. Find the characteristic function and the first two moments.
Let X be a (continuous) uniform random variable on the interval [0,1] and Y be an exponential random variable with parameter lambda. Let X and Y be independent. What is the PDF of Z = X + Y.
An experiment consists of randomly drawing 3 cards from a standard deck (without replacement). The random variable Z is defined to be 2 times the number of face cards drawn which are not aces (jacks, queens, or kings). Find the density function of Z.
Suppose that X and Y are independent and uniformly distributed random variables. Range for X is (−1, 1) and for Y is (0, 1). Define a new random variable U = XY, then find the probability density function of this new random variable.

SEE MORE QUESTIONS

Recommended textbooks for you

Calculus For The Life Sciences

Calculus

ISBN:

9780321964038

Author:

GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:

Pearson Addison Wesley,

Calculus For The Life Sciences

Calculus

ISBN:

9780321964038

Author:

GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:

Pearson Addison Wesley,

SEE MORE TEXTBOOKS