Question

The probability density function for a random variable X is given by f(x) = x 18 , 0 < X < 6. Use this pdf to find the following probabilities. (Hint: draw the pdf and remember that probability = area.) a. Find P(X < 1). (4 points) b. Find P(X > 4). (6 poin

Answer 1

Answer:

a) 0.0278

b) 0.5556

Step-by-step explanation:

We are given the following in the question:

The probability density function for a random variable X is given by

$f(x) = \displaystyle\frac{x}{18}\\\\0 < x < 6$

We can find the probabilities as:

$P(Xc) = \displaystyle\int^{\infty}_c f(x) dx$

a) P(X < 1)

$P(X$

b) P(X > 4)

$P(X>4) = \displaystyle\int^{\infty}_4 f(x) dx\\\\P(X>4) = \displaystyle\int^{6}_4 \frac{x}{18} dx\\\\= \frac{1}{18}\displaystyle\int_{4}^6 x~ dx = \frac{1}{18}\Big[\frac{x^2}{2}\Big]^6_4\\\\= \frac{1}{18}\Big(\frac{36}{2}-\frac{16}{2}\Big) = \frac{1}{36}\Big(10\Big) = \frac{10}{18} = 0.5556$