Question

The random variable x has a p.d.f. given by: f(zfor 0 2 Find the UPPER quartile, Q3 O 0.5 O 0.375 0.75 1.5 Given the following joint probability distribution of X and Y 10.0450.08l10.1 Then X + Y takes on values 2,3,4,5, and 6. Build the probability distribution for Z = X + Y by matching the appropriate probability to each value of Z. 1. 0.16 2. 0.215 3. 0.27 4. 0.045 5. 0.315

Answer 1

The upper quartile of the PDF f(x) is the value of F(x) at x= 0.75

Now F(x) is $\int$f(x) dx = (1/2)*x

So, F(0.75) = 0.75/2 = 0.375

So option b is correct.

2. We know the total probability must be equal to 1. From the table we can see that this is satisfied.

Now, Z will take the value 2 when both x and y are 1 so the required probability is 0.045

Z will be 3 when x=1 and y=2 or x= 2 and y=1. So the required probability is 0.08+0.08 = 0.16

Z will be 4 when both x and y are 2 or x=3, y=1 or x=1,y=3. So the required probability is 0.14+0.05+0.125 = 0.315

Similarly probability for Z=5 is 0.14+0.075 =0.215

And Probability for Z=6 is 0.27