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

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