Solve your IGNOU Doubts

Question:

The following table represents the joint probability distribution of the discrete random variable

X	Y	1	2	3
1		0.2	0.2	0.1
2		0.1	0.3	0.1

Find

a) The marginal distributions.

b) The conditional distribution of Y given X = 2

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Question:

An insurance company insured 2000 scooter drivers, 3000 car drivers and 5000 truck
drivers. The probabilities that scooter, car and truck drivers meet an accident are 0.02, 0.04, and 0.25 respectively. One of the insured persons meets with an accident. What is the probability that he is a
a) Scooter driver
b) Car driver

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Question:

Determine the constant k such that the function $f(x) = kx^2(1-x)^5, 0<x<1$ is a beta distribution of first kind. Also, find its mean and variance

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Question:

An insurance company selected 6000 drivers from a city at random in order to find a
relationship between age and accidents. The following table shows the results to these 6000 drivers.

Age of drivers (in years) Class Interval	Accidents in one year
	0	1	2	3	4 or more
18 – 25	700	310	225	110	85
25 – 40	1100	290	200	105	80
40 – 50	1200	235	175	80	55
50 and above	600	205	140	70	35

If a driver from the city is selected at random, find the probability of the following events:
a) Age lying between 18 – 25 and meet 3 accidents
b) Age lying between 18 – 40 and meet 1 accident
c) Age more than 25 years and meet at most one accident
d) Having no accident in the year
e) Age lying between 18 – 40 and meet at least 3 accidents

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Question:

Which of the following statements are true or false? Give reason in support of your answer.

a) When two dice are thrown simultaneously then total number of sample points in the
sample space will be 12.
b) Expected value of a continuous random variable X is defined as
$E(x) = \int_{\infty }^{x}xf(x) dx$
.
c) If X and Y are independent random variable then $V(X - Y) = V(X) - V (Y)$ .
d) If $X \sim B(4,3)$ then variance of X is 12.
e) If probability density function of a normally distributed random variable X is
$f(x) = \frac{1}{6\sqrt{2\pi}}e^{\frac{1}{2}\left ( \frac{x-46}{6} \right )^2}$ , $- \infty <x<\infty$
then variance of X is 36.