Let X1, X2, ..., Xn be independent random variables and Y = min{X1, X2,..., Xn}. n Fy(y) = 1 – II (1 – Fx,(y)) i=1 (a) A certain electronic device uses 5 batteries, with each battery to have a life that is exponentially distributed with mean of 48 hours and is independent of the life of other batteries. If the device fails as soon as at least one of its batteries fail, what is the expected life of the device?

Let X1, X2, ..., Xn be independent random variables and Y = min{X1, X2,..., Xn}. n Fy(y) = 1 – II (1 – Fx,(y)) i=1 (a) A certain electronic device uses 5 batteries, with each battery to have a life that is exponentially distributed with mean of 48 hours and is independent of the life of other batteries. If the device fails as soon as at least one of its batteries fail, what is the expected life of the device?

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.

Chapter2: Exponential, Logarithmic, And Trigonometric Functions

Section2.CR: Chapter 2 Review

Problem 111CR: Respiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data...

See similar textbooks

Similar questions

Respiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data are at or below for respiratory rates in breath per minute during the first 3 years of infancy are given by y=101.82411-0.0125995x+0.00013401x2 for awake infants and y=101.72858-0.0139928x+0.00017646x2 for sleeping infants, where x is the age in months. Source: Pediatrics. a. What is the domain for each function? b. For each respiratory rate, is the rate decreasing or increasing over the first 3 years of life? Hint: Is the graph of the quadratic in the exponent opening upward or downward? Where is the vertex? c. Verify your answer to part b using a graphing calculator. d. For a 1- year-old infant in the 95 th percentile, how much higher is the walking respiratory rate then the sleeping respiratory rate? e. f.
A random variable X has only two values a and b with P(X = a) = p , P(X = b) = q (p + q = 1).Find its mean value and variation.
If X is a Poisson variable such that P(X =2) = 9P(X= 4) + 90P(X = 6), find the mean and variance of X.
Show that variance o? = (x²) – ((x))²
An ordinary (fair) coin is tossed 3 times. Outcomes are thus triple of “heads” (h) and tails (t) which we write hth, ttt, etc. For each outcome, let R be the random variable counting the number of tails in each outcome. For example, if the outcome is hht, then R (hht)=1. Suppose that the random variable X is defined in terms of R as follows X=6R-2R^2-1. The values of X are given in the table below. A) Calculate the values of the probability distribution function of X, i.e. the function Px. First, fill in the first row with the values X. Then fill in the appropriate probability in the second row.
3(6x - x) Determine the mean and variance of the random variable for f(x) = 0
A random variable X takes values 0,1,2 where E(x) =1.5, var(x)=0.25 then E (3x– x² +4) =
In statistics, the range is computed as the difference between the minimum and maximum values Range(x) = Max(x) - Min(x) If the operatinal time of KAL CULAS graphics cards are each exponentially distribitued with a mean time of 32 months, compute the expected range of i.i.d. random variables X1, X2, X3, X4; where each random variable represents one graphics card to show your work set up all integrals correctly.
Many people believe that the daily change in price of a company's stock in the stock market is a random variable with mean 0 and variance o² during the middle 2 months between 2 earning report dates when there is not much news released. That is, if Yn represents the closing price of the stock on the nth trading day of that period, then Yn = Yn-1+Xn, for 1 ≤ n ≤ 60, where X₁, X2,..., X60 are independent and identically distributed random variables with mean 0 and variance o². Suppose that the stock price at the beginning of the 2-month period is 100. If o = 2, what is the approximate probability that the stock's closing price on the 30th trading day will exceed 110, i.e., what is P(Y30 > 110)
(8) Find the variance of X when X is distributed as N(0, 1). The correct answer is -1 1 N/A (Select One)