An important factor in solid missile fuel is the particle size distribution. significant problems occur if the particle sizes are too large. from production data in the past, it has been determined that the particle size (in micrometers) distribution is characterized by 3x−4, x > 1, f(x) = 0, elsewhere. (a) verify that this is a valid density function. (b) evaluate f(x). (c) what is the probability that a random particle from the manufactured fuel exceeds 4 micrometers?

b)

c) 0.0156

Step-by-step explanation:

Let's call X : '' Particle size (in micrometers) ''

X is a random variable

The distribution function for X is :

For x > 1

f(x) = 0, elsewhere

For a) the condition for f(x) to be a valid density function is that

the integral between -∞ and ∞ of f(x) must be equal to 1.

For the integral I change ∞ for j so ∞ = j

Also for the integral I change -∞ for k so k = -∞

Then f(x) is a valid density function

b) To find F(x) we must integrate between -∞ and x the function f(t)

We calculate f(t) changing x by t in the f(x) function

Now we integrate

c) P(X>4)

P(X>4) = 1 - P(X≤4)

P(X>4) = 1 - F(4)

answer: 42

use a calculator to find that 845/73 = 11.575

the whole part of the answer is 11. multiply this by 73 to get 11*73 = 803.

subtract that result from 845 to get 845 - 803 = 42

i think the length is 12 and the width is 17