# Thread: Small DRV question [S1]

1. ## 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

2. 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?