𝑋
)
So
𝑠
.
𝑑
. (
𝑌
) = [
𝑣𝑎𝑟
(
𝑌
)]
1
2
=
√
1.1375
= 1.067
.
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0
1
2
3
4
5
Probability
Number of increases
Stock index increases over 5 years

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4.
In each of the following cases
X
is a count. Does it have a binomial
distribution? Justify you answer in each case.
(a)
You observe the sex of the next 20 babies born at a local hospital;
X
is
the number of girls among them.
Yes
•
Recall our concerns about the gender composition example used in lectures:
the fertility decision about whether to have a third child or not being
impacted by the gender mix of the first two children; possibility of multiple
births. These are not relevant here.
•
Independence across trials now refers to births to different women and
having a girl is not contagious!
(b)
A couple decides to continue to have children until their first girl is
born;
X
is the total number of children the couple has.
No
•
Here n is not fixed and depends on previous trial outcomes.
5.
The amount of petrol sold daily by a service station is known to be
uniformly distributed between 4,000 and 6,000 litres.
What is the
probability of sales on any one day being between 5,500 and 6,000 litres?
𝑓
(
𝑥
) =
1
2000
𝑖𝑓
4000
≤ 𝑥 ≤
6000
= 0
𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
∴ 𝑃
(5500
≤ 𝑋 ≤
6000) = 500/2000 = 0.25