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) =x f (x)dx
c) If X and Y are independent random variable then V(X – Y) = V(X) – V (Y).
d) If X ~ B(4,3) then variance of X is 12.
e) If probability density function of a normally distributed random variable X is , - ∞ <x< ∞
then variance of X is 36.
a) False. The total number of sample points in the sample space ____ __________ _____ __________ ________ ______ ___ ___ ___ ________ _________ _____.
__________ _________ ______ ____ _____ ________ _________ ____ _____ ________.
___ __________ ___ ___ _________ ____.
____ __________ _____ __________ __________ ____.
_______ _____ ________ ________ _______.
________ ___ ________ _____ ______ ___ __________ _____ ________ _____ ______.
_______ ____ _____ ____ _____ _____ ________ ______ __________ ____ ___ __________.
___.
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The following table represents the joint probability distribution of the discrete random variable (X, Y):
| Y X | 1 | 2 | 3 |
| 1 | 0.2 | 0.2 | 0.1 |
| 2 | 0.1 | 0.3 | 0.1 |
Events A, B, C are mutually exclusive and exhaustive. If odds against A are 4 :1and against B are 3: 2 . Find the odds against event C.
If the probability that an individual suffers a bad reaction from an injection of a given serum is 0.002, determine the probability that out of 400 individuals
(i) exactly 2
(ii) more than 3
(iii) at least one
individuals suffer from bad reaction.
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) =x f (x)dx
c) If X and Y are independent random variable then V(X – Y) = V(X) – V (Y).
d) If X ~ B(4,3) then variance of X is 12.
e) If probability density function of a normally distributed random variable X is , - ∞ <x< ∞
then variance of X is 36.
A rain coat dealer can earn Rs 800 per day during a rainy day. If it is a dry day, he can lose Rs 150 per day. What is his expectation, if the probability of rain is 0.6?
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
A player tosses two unbiased coins. He wins Rs. 10 if 2 heads appear, Rs. 5 if one head appears and Rs 1 if no head appears. Find the expected value of the amount won by him.