Question

Question 1

Refer to the probability function given in the following table for a
random variable X that takes on the values 1,2,3 and 4
X 1 2 3 4
P(X=x) 0.4 0.3 0.2 0.1
a) Verify that the above table meet the conditions for being a discrete probability
distribution
b) Find P(X<2)
c) Find P(X=1 and X=2)
d) Graph P(X=x)
e) Calculate the mean of the random variable X
f) Calculate the standard deviation of the random variable X

Question 2

Graph P(X=x) for binomial distributions with the following parameters
a) ? = 4 ??? ? = 0.5
b) ? = 4 ??? ? = 0.3
c) ? = 4 ??? ? = 0.1
d) Which if any of the graphs in part a-c are symmetric?
e) Without actually constructing the graph, would the case
? = 10 ??? ? = 0.5 be symmetric or skewed?
f) Which of the graphs in part a-c is the most heavily skewed?
g) Without actually constructing the graph, would the case ? = 4 and
? = 0.01 exhibit more or less skewness than the graph in part(c)?

Question 3

Suppose that a random variable y has a Poisson distribution.
Compute the following probabilities
a) P(y = 4) given ? = 3
b) P(y<4) given ? = 3
c) P(y<=4) given ? = 3
d) P(y>4) given ? = 3
e) P(2<y<5) given ? = 3

Question 4

The number of calls coming to the customer care center of a mobile company per
minute is a Poisson random variable with mean 5. Find the probability that no call
comes in a certain minute

Answer 1

Question 1

Refer to the probability function given in the following table for a
random variable X that takes on the values 1,2,3 and 4
X 1 2 3 4
P(X=x) 0.4 0.3 0.2 0.1
a) Verify that the above table meet the conditions for being a discrete probability
distribution
b) Find P(X<2)
c) Find P(X=1 and X=2)
d) Graph P(X=x)
e) Calculate the mean of the random variable X
f) Calculate the standard deviation of the random variable X

a)If sum of all probabilities is one then we say that it is discrete probability distribution.

x	P(x)
1	0.4
2	0.3
3	0.2
4	0.1
Total	1

b)

P(X < 2) = P(X = 1) = 0.4

c)

P(X = 1 and X = 2) = P(X = 1)*P(X = 2) = 0.4*0.3 = 0.12

d)

The graph of P(X = x)

e)

The mean of the random variable X is:

x	P(x)	x*P(X)
1	0.4	0.4
2	0.3	0.6
3	0.2	0.6
4	0.1	0.4
Total	1	2

f) The standard deviation of random variable X:

x	P(x)	x*P(X)	x^2*P(x)
1	0.4	0.4	0.4
2	0.3	0.6	1.2
3	0.2	0.6	1.8
4	0.1	0.4	1.6
Total	1	2	5

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