# Small DRV question [S1]

• May 14th 2009, 08:07 AM
db5vry
Small DRV question [S1]
The probability distribution of the discrete random variable X is given in the following:
For x = 1, 2, 3, 4, 5.
P(X=x) = 0.3, p, 0.1, q, 0.05.

(a) Show that p + q = 0·55. [1]
(b) Given that E(X) = 2·75, show that p = 0·15 and q = 0·4. [4]
(c) Find the variance of X. [3]
(d) The random variable Y is defined by Y = 4X + 2.
(i) Find the mean and variance of Y.
(ii) Find P(Y < 15). [6]

I have got all the way to the second part of (d).
for c, I calculated the variance of X to be 1.8875.
for d1] the mean was 14 and the variance was 30.2.

How is P(Y < 15) found?
It's probably something very simple. Thank you if you can steer me in the right direction as to what it is :)
• May 14th 2009, 04:23 PM
mr fantastic
Quote:

Originally Posted by db5vry
The probability distribution of the discrete random variable X is given in the following:
For x = 1, 2, 3, 4, 5.
P(X=x) = 0.3, p, 0.1, q, 0.05.

(a) Show that p + q = 0·55. [1]
(b) Given that E(X) = 2·75, show that p = 0·15 and q = 0·4. [4]
(c) Find the variance of X. [3]
(d) The random variable Y is defined by Y = 4X + 2.
(i) Find the mean and variance of Y.
(ii) Find P(Y < 15). [6]

I have got all the way to the second part of (d).
for c, I calculated the variance of X to be 1.8875.
for d1] the mean was 14 and the variance was 30.2.

How is P(Y < 15) found?
It's probably something very simple. Thank you if you can steer me in the right direction as to what it is :)

I haven't checked your calculations - I assume you know what you're doing and can do basic arithmetic.

As to the specific question you've asked ..... What values of X will make Y < 15? What's the probability of getting those values of X?