The life expectancy (in years) of a certain brand of clock radio is a continuous random variable with the probability density function below. f(x) = { 2/x+22 #x20 otherwise (A) Find the probability that a randomly selected clock lasts at most 6 years. (B) Find the probability that a randomly selected clock radio lasts from 6 to 11 years. (C) Graph y = f(x) for [0, 11] and show the shaded region for part (A).

The life expectancy (in years) of a certain brand of clock radio is a continuous random variable with the probability density function below. f(x) = { 2/x+22 #x20 otherwise (A) Find the probability that a randomly selected clock lasts at most 6 years. (B) Find the probability that a randomly selected clock radio lasts from 6 to 11 years. (C) Graph y = f(x) for [0, 11] and show the shaded region for part (A).

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.6: Exponential And Logarithmic Equations

Problem 70E

See similar textbooks

Similar questions

Recall that the general form of a logistic equation for a population is given by P(t)=c1+aebt , such that the initial population at time t=0 is P(0)=P0. Show algebraically that cP(t)P(t)=cP0P0ebt .
9.1) Suppose X1, X2, and X3, denotes a random sample from the exponential distribution with density function shown in the image. a) Which of the above estimators are unbiased for θ? b) Among the unbiased estimators of θ, which has the smallest variance?
suppose x has an exponential distribution with probability density function f(x) =2e^-2x, x>0. Then P(X>1)
Suppose that a study of a certain computer system reveals that the response time, in seconds, has an exponential distribution with density curve f(x) = (1/3)e(-x/3) for x > 0 and f(x) = 0 otherwise. What is the probability that response time exceeds 5 seconds? What is the probability that response time exceeds 10 seconds?
Suppose that n observations are chosen at random from a continuous pdf fY(y). What is the probability that the last observation recorded will be the smallest number in the sample? I asked this question earlier today, but didn't quite understand all of the response. P(y1<=yn)p(y2<=yn) and so on was used, but shouldn't the yn be listed first in the inequality since we want to know if yn is the smallest?
Suppose that x has an exponential distribution with θ =1.5. Find P(x > 1
The time for the first widget to be manufactured each morning is random between 1 and 3 seconds with a pdf of f(x)=1/162(x-3)^2(x+6) for 0 < x < 6What is the cumulative distribution function, F(x)? What is the probability of a widget being made earlier than 4 s?Answer to four decimal places What is the probability of a widget being made later than 1.3 s?Answer to four decimal places
If the probability mass function of the variable X described in the table is. find variance Y=x^2+4x If you know that the torque is of the second order of the variable X about the origin is equal to 2.85
The lifetime of a certain type of TV remote control is given by Y . Suppose Y has approximately exponential distribution with mean 8 years. a) Find the probability that a remote control of this type will last more than 15 years. b) Find the probability that of eight such remote controls at least one will last more than 15 years. c) What should the warranty period for these remote controls be if the manufacturer wants 85% of the remote controls to last beyond the warranty period? d) What is the moment generating function of Y .
If the probability density of X is given by f(x) =2x−3 for x > 10 elsewherecheck whether its mean and its variance exist.
1.9.5. Let a random variable $X$ of the continuous type have a pdf $f(x)$ whose graph is symmetric with respect to $x=c .$ If the mean value of $X$ exists, show that $E(X)=c$Hint: Show that $E(X-c)$ equals zero by writing $E(X-c)$ as the sum of two integrals: one from $-\infty$ to $c$ and the other from $c$ to $\infty .$ In the first, let $y=c-x$ and, in the second, $z=x-c .$ Finally, use the symmetry condition $f(c-y)=f(c+y)$ in the first.
If X is an exponential random variables with rate 1, then its distribution function is given by F(x) = 1 − e−x Show that x = − ln(1 − u).