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# Random Variables

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30)Let X be a Poisson random variable with parameter (lambda). Show that P {X=i} increases monotonically and then decreases monotonically as i increases, reaching its maximum when i is the largest integer not exceeding (lambda).
Hint: Consider P{X=i}/P{X=i-1}.

37) Let X1, X2, ...., Xn be independent random variables, each having a uniform distribution function of M, Fm (.), is given by
Fm(x)=x^n, 0(less than or equal to)x(less than or equal to) 1
What is the probability density function of M?

40) Suppose that two teams are playing a series of games, each of which i s independently won by team A with probability p and by team B with probability 1-p. The winner of the series is the first team to win four games. Find the expected number of games that played, and evaluate this quantity when p=1/2.

##### Solution Summary

The solution addresses random variables as follows - 30)Let X be a Poisson random variable with parameter (lambda). Show that P {X=i} increases monotonically and then decreases monotonically as i increases, reaching its maximum when i is the largest integer not exceeding (lambda).
Hint: Consider P{X=i}/P{X=i-1}.

37) Let X1, X2, ...., Xn be independent random variables, each having a uniform distribution function of M, Fm (.), is given by
Fm(x)=x^n, 0(less than or equal to)x(less than or equal to) 1
What is the probability density function of M?

40) Suppose that two teams are playing a series of games, each of which i s independently won by team A with probability p and by team B with probability 1-p. The winner of the series is the first team to win four games. Find the expected number of games that played, and evaluate this quantity when p=1/2.

##### Measures of Central Tendency

This quiz evaluates the students understanding of the measures of central tendency seen in statistics. This quiz is specifically designed to incorporate the measures of central tendency as they relate to psychological research.

##### Measures of Central Tendency

Tests knowledge of the three main measures of central tendency, including some simple calculation questions.