Question

please answer the last part "the probability that at least one out of 3 devices of this type will function for at least 42 months:"

(1 point) The probability density function of X, the lifetime of a certain type of device (measured in months), is given by 0 if x s 15 f(x)= if x> 15 Find the following: P(X> 18) 5/6 The cumulative distribution function of X: 0 if xs 15 F(x) 15/x +1 if x> 15 The probability that at least one out of 3 devices of this type will function for at least 42 months

Answer 1

TOPIC:Binomial distribution.

a Define x The lifetime of the centain - type of device (measured in month The pdf of x is given as sex) = {o } x 215 1 16 X > 15 4 Requined part of the question :- Now, we have =) p. = P (of a device will function) at least 42 months. = P(x + 42). I Nx) dx. - 42 = 15. = 15. = 15.

Hene, n = No. of devices - 3. xet, aya No. of devices that will function for at least 42 months. y Bin (n= 3, p = 162). The pmf of y is - P (1=Y) = { 3-7 Jon, y=0,1,2,3. otherwise. We need, plr is at least 1. = P(x2). = 1-P (red. = 1-P (y=0), = 1-(3) (4) (27. *1- (22) 2015 2015 2744 o. 7343 'Rounded to I dour decimals E and