Question

# Let X be a continuous random variable with the probability density function f(x) = C x,...

Let X be a continuous random variable with the probability density function f(x) = C x, 6 ≤ x ≤ 25, zero otherwise.

a. Find the value of C that would make f(x) a valid probability density function. Enter a fraction (e.g. 2/5): C =

b. Find the probability P(X > 16). Give your answer to 4 decimal places.

c. Find the mean of the probability distribution of X. Give your answer to 4 decimal places.

d. Find the median of the probability distribution of X. Give your answer to 4 decimal places.

(a) C is got by noting that the Total Probability = 1.

So,

we get:

between the limits 6 to 25.

Applying linits, we get:

So,

C = 2/589

(b)

The Probability Density Function of X is given by:

,

6 X 25

between the limts 16 to 25.

Applying limits, we get:

P(X>16) = 0.6265

(c)

The mean E(x) is given by:

,

between the limits 6 to 25.

Applying limits, we get:
E(X) = 17.4409

(d)

The median got as follows:

between the limits 6 to x.

Applying limits, we get:

So,

x= 18.1797

#### Earn Coins

Coins can be redeemed for fabulous gifts.

##### Need Online Homework Help?

Most questions answered within 1 hours.

##### Active Questions
• In your travels or readings, what branding strategies, activities or identifiers have major U.S. brands altered...
• Find the mean of the data summarized in the given frequency distribution. Compare the computed mean...
• Prove that √3 is irrational. You may use the fact that n2 is divisible by 3...
• You are the vice president of a 60-bed cardiac hospital. Last year your hospital generated about...
• A company has an 11% WACC and is considering two mutually exclusive investments (that cannot be...
• Century National Bank has offices in several cities in the Midwest and the southeastern part of...