Statistics for Economics : Assignment 2
1. Suppose two unbiased dice are rolled. Let Xdenote the absolute value o the difference
between the two numbers that appear. Determine and then sketch the probability
function of X.
2. Suppose a fair coin is tossed 10 times independently. Determine the probability func-
tion of the number of heads that will be obtained.
3. Suppose the p.d.f. of a ransom variable Xis:
f(x) = 1
36 (9 −x2) for −3≤x≤3 and f(x) = 0 otherwise. Sketch the p.d.f. and
determine the following probabilities:
(a) P(X < 0)
(b) P(−1≤X≤1)
(c) P(X > 2)
4. Show that there does not exist any number csuch that the following function would
be a probability function:
f(x) = c
xfor x= 1,2, ... and f(x) = 0 otherwise.
5. Show that there does not exist any number csuch that the following function would
be a p.d.f.:
f(x) = c
xfor 0 <x<1 and f(x) = 0 otherwise.
6. Suppose a coin is tossed repeatedly until a head is obtained for the first time. Let X
denote the number of tosses that are required. Draw the c.d.f. of X.
7. Suppose the c.d.f. of a random variable Xis given by:
F(x) = 0 for x≤0; F(x) = 1
9x2for 0 < x ≤3 and F(x) = 1 for x > 3.
Find and draw the p.d.f. of X.
8. Verify if the following graph in Figure 1 below is a valid c.d.f. If yes, then clearly state
the corresponding p.d.f.:
9. Provide an example of a p.d.f. whose c.d.f. is right continuous, but is not continuous.
10. A non-negative integer-valued random variable has c.d.f. given by F(x)=1−(1/2)x+1
for x= 0,1,2, ... and zero is x < 0.
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