HSC Commerce Class 12 - Tamil Nadu Board of Secondary Education Question Bank Solutions for Business Mathematics and Statistics

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If X is a discrete random variable and p(x) is the probability of X, then the expected value of this random variable is equal to

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Which of the following is not possible in probability distribution?

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A discrete probability distribution may be represented by

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A probability density function may be represented by

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E[X – E(X)] is equal to

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E[X – E(X)]² is

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`int_(-oo)^oo` f(x) dx is always equal to

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A listing of all the outcomes of an experiment and the probability associated with each outcome is called

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If p(x) = `1/10`, x = 10, then E(X) is

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An expected value of a random variable is equal to it’s

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A discrete probability function p(x) is always non-negative and always lies between

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The distribution function F(x) is equal to

Prove that if E(X) = 0, then V(X) = E(X²)

What is the expected value of a game that works as follows: I flip a coin and if tails pay you ₹ 2; if heads pay you ₹ 1. In either case, I also pay you ₹ 0.50

Prove that V(aX) = a²V(X)

Prove that V(X + b) = V(X)

The time to failure in thousands of hours of an important piece of electronic equipment used in a manufactured DVD player has the density function
f(x) = `{{:(2"e"^(-2x)",",  x > 0),(0",",  "otherwise"):}`
Find the expected life of this piece of equipment

Mention two branches of statistical inference

What is an estimator?

What is an estimate?