Probability and Statistics
Hints/Solutions to Assignment No. 3
4 3 4
+
2 1 3 22
1. P(Ruby wins) =
.
=
35
7
3
2. Suppose n missiles are fired and X is the number of successful hits. Then
X ~ Bin(n, 0.75). We want n such that P(X 3) 0.9 5, or P(X = 0) +
Probability and Statistics
Hints/Solutions to Assignment No. 2
1. (a) No, as it is not continuous from right at x = .
(b) No, lim F(x) 0, lim F(x) 1.
x
x
(c) Yes
(d) Yes
1
2. P X
2
5
5
1 11 1 19
=
.
= F F =
2
2
2 24 8 24
311
P(1 < X < 2) = F(2) F(1)
Probability and Statistics
Assignment No. 2
1.
Check if the following functions define cdf's :
(a) F(x) = 0, if x < 0, = x, if 0 x 1/2, and
= 1, if x > 1/2.
-1
(b) F(x) = (1/) tan x, - < x < .
(c) F(x) = 0 , if x 1, and = 1- (1/x), if x > 1.
(d) F(x) = 1
Probability and Statistics
Hints/Solutions to Assignment No. 1
5
5 4 3!
2 = 48 0.384.
1. Required probability
=
=
55
125
2. Use definitions.
3. Let A 5 appears, B even number appears. Then
A = cfw_(1, 4), (2, 3), (3, 2), (4, 1). Also B will have 18 eleme
Probability and Statistics
Assignment No. 3
1. Ruby and Mini tied for the first place in a beauty contest. The winner is to be
decided by the majority opinion of a panel of three judges chosen at random from
a group of seven judges. If four of these judge
Probability and Statistics
Assignment No. 1
1. If 5 balls are placed at random into 5 cells, find the probability that exactly one
cell remains empty.
2. Let event E be independent of events F, F G and F G . Show that E is
independent of G.
3. A pair of d