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![2. L
3.
] Suppose the c.d.f. of a random variable X is defined as
if x < 0
if 0 < x < 1
if 1 ≤ x < 2
if x ≥ 2
Find each of the following probabilities.
(a) P(X= 2)
F(x) =
Find the c.d.f of X.
0
x²/4
2x/5
1
Find E(X) and Var(X).
(b) P(X ≥ 1)
Suppose the p.d.f. of a random variable X is defined as
x²/63 if 3 ≤x≤6
otherwise
(c) P(1/2 < X ≤ 2)
f(x) =
= {x²/63
Let the probability density function of a continuous random variable X be defined a
f(x) = {x²/9
if 0 ≤ x ≤ 3
otherwise
4. In a school, the height of all male students has an approximately normal distribution with the
mean of 178 cm and the standard deviation of 3 cm.
(a)
3] When a male student in the school is randomly surveyed, what is probability
that he is below 180 cm?
(b)
When 16 male students in the school are randomly surveyed, what is the
probability that their average height is above 179 cm?
5. In a supermarket, there are chicken eggs and duck eggs. Assume the weight of each type of
eggs is normally distributed. The chicken eggs have a mean of 50 grams and a standard
deviation of 3 grams; the duck eggs have a mean of 60 grams and a standard deviation of 5
grams.
When a chicken egg and a duck egg are randomly chosen, estimate the
probability that the duck egg weights more than a chicken egg.
(b)
When two chicken eggs and three duck eggs are randomly chosen, estimate
the probability that their total weight is between 275 and 300 grams.](https://content.bartleby.com/qna-images/question/e8f98c03-2dea-45fe-9e7d-c001811b98bd/cc470a86-845e-4a5d-98b6-6128186eea37/pjiq90e_processed.jpeg)
