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Problem 1 The pdf of X, the lifetime of a certain type of electronic device in...
Let X be the lifetime of a certain type of electronic device (measured in hours). The probability density function of X is f(x) =10/x^2 , x > c 0, x ≤ c (a) Find the value of c that makes f(x) a legitimate pdf of X. (b) Compute P(X < 20).
Problem 4. The life X, in hours, of a certain device, has a pdf 100 0, < 100 (a) What are the probability that this device will survive 150 hours of operation? (b) Find the life expectancy of the device.
Problem 4. The median of a PDF fx(x) is defined as the number a for which P(X s a)-P(X > a)-1/2. Find the median of a Gaussian PDF N(μ; σ2).
The probability density function of X, the lifetime of a certain type of electronic device (measured in hours), is given by fX(x) = ( C/x^2 x>5 0 x<5 where C>0 is a constant which needs to be determined. (i) What is the probability that the device’s lifetime is 10 hours? (ii) Find the 25%th quantile of X? (iii) If the device lifetime is X, then its total electricity cost equals . What is the expected total electricity cost of the...
2) The lifetime in years of a certain type of electronic component has a probability density function given by: otherwise a) If the expected value of the random variable is 3/5 i.e. E(X)-3/5, find a and b. b) Show that the median lifetime is approximately 0.6501 years.
Problem 4. The life X, in hours, of a certain device, has a pdf 100 , t 100 0, t< 100 (a) What are the probability that this device will survive 150 hours of operation? (b) Find the life expectancy of the device.
Thank you! 1) Let X be the life (in hours) of a certain electronic device. The pdf of X is f(x)- e-100, for x ? 0 and 0 otherwise. What is the expected life of this device? 100 2) The density function of coded measurements of the pitch diameter of threads of a fitting is 4 0 elsewhere. Find the expected value of X
3. Let X has the following pdf: {. -1 <1 fx(a) otherwise 1. Find the pdf of U X2. 2. Find the pdf of W X
1. Let X be a random variable with pdf f(x )-, 0 < x < 2- a) Find the cdf F(x) b) Find the mean ofX.v c) Find the variance of X. d) Find F (1.75) e) Find PG < x < +' f) Find P(X> 1). g) Find the 40th percentile.*
The random Variable X has a pdf fx (2) = {*** kr + > -1 <r<2 otherwise Y is a function of X and is derived using Y = g(x) = X S -X X2 X <0 X>0 Find: (A) fr(y) (B) E[Y] using fy(y) (C) EY] using fx (2)