Question

In: Statistics and Probability

Let f(x) = a(e-2x – e-6x), for x ≥ 0, and f(x)=0 elsewhere. a) Find a...

Let f(x) = a(e-2x – e-6x), for x ≥ 0, and f(x)=0 elsewhere.

a) Find a so that f(x) is a probability density function

b)What is P(X<=1)

Expert Solution

(a)
The value of a is found by noting that the Total Probability = 1

So,

we get:

i.e.,

between the limits 0 to .

Applying limits, we get:

i.e.,

So

a = 3

Answer is:

3

(b)

So, the Probability Density Function of X is written as follows:

So,

between the limits 0 to 1

Applying limits, we get:

= 0.7982

So,

Answer is:

0.7982

orchestra answered 1 year ago

Let X be an exponential distribution with mean=1, i.e. f(x)=e^-x for 0<X< ∞, and 0 elsewhere....

Let X be an exponential distribution with mean=1, i.e. f(x)=e^-x for 0<X< ∞, and 0 elsewhere. Find the density function and cdf of a) X^1/2 b)X=e^x c)X=1/X Which of the random variables-X, X^1/2, e^x, 1/X does not have a finite mean?

Let f(x) = (x − 1)2, g(x) = e−2x, and h(x) = 1 + ln(1 − 2x). (a) Find the linearizations of f, g, and h at a =...

Let f(x) = (x − 1)2, g(x) = e−2x, and h(x) = 1 + ln(1 − 2x). (a) Find the linearizations of f, g, and h at a = 0. Lf (x) = Lg(x) = Lh(x) = (b) Graph f, g, and h and their linear approximations. For which function is the linear approximation best? For which is it worst? Explain. The linear approximation appears to be the best for the function ? f g h since it is closer to ? f g h for a larger domain than it is to - Select - f and g g and h f and h . The approximation looks worst for ? f g h since ? f g h moves away from L faster...

For the function f(x) = x^2 +3x / 2x^2 + 6x +3 find the following, and...

For the function f(x) = x^2 +3x / 2x^2 + 6x +3 find the following, and use it to graph the function. Find: a)(2pts) Domain b)(2pts) Intercepts c)(2pts) Symmetry d) (2pts) Asymptotes e)(4pts) Intervals of Increase or decrease f) (2pts) Local maximum and local minimum values g)(4pts) Concavity and Points of inflection and h)(2pts) Sketch the curve

1. Find the critical numbers for the following functions (a) f(x) = 2x 3 − 6x...

1. Find the critical numbers for the following functions (a) f(x) = 2x 3 − 6x (b) f(x) = − cos(x) − 1 2 x, [0, 2π] 2. Use the first derivative test to determine any relative extrema for the given function f(x) = 2x 3 − 24x + 7

find the line tangent to graph of f(x) at x=0 1) f(x)=sin(x^2+x) 2)f(x)=e^2x+x+1

Find f. f ''(x) = 4 + 6x + 24x2, f(0) = 4, f (1) = 12

Find f(x) for the following function. Then find f(6), f(0), and f(-7). f(x)=-2x^2+1x f(x)= f(6)= f(0)=...

Find f(x) for the following function. Then find f(6), f(0), and f(-7). f(x)=-2x^2+1x f(x)= f(6)= f(0)= f(-7)=

Let f(x) = {(C/x^n if 1≤ x <∞; 0 elsewhere)} where n is an integer >1....

Let f(x) = {(C/x^n if 1≤ x <∞; 0 elsewhere)} where n is an integer >1. a. Find the value of the constant C (in terms of n) that makes this a probability density function. b. For what values of n does the expected value E(X) exist? Why? c. For what values of n does the variance var(X) exist? Why?

1) Find f(x) by solving the initial value problem. f' (x) = e x − 2x;...

1) Find f(x) by solving the initial value problem. f' (x) = e x − 2x; f (0) = 2 2) A rectangular box is to have a square base and a volume of 20f t^3 . If the material for the base costs 30¢/f t^2 , the material for the sides costs 10¢/ft^2 , and the material for the top costs 20¢/f t^2 , determine the dimensions of the box that can be constructed at minimum cost.

Find all functions f(x) with f′′(x) = 3x^3 − 2x^2 + x, f(0) = 1, and...

Find all functions f(x) with f′′(x) = 3x^3 − 2x^2 + x, f(0) = 1, and f(1) = 1.