The random variable X has the geometric distribution with probability mass function (pmf)Py(x) = q*p. x = 0,1, 2, ... 0 x).|A7The random variable X has the binomial distribution with probability mass function() p*(1 - p)²-*,x = 0, 1,2; 0

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A 5 The random variable X has the geometric distribution with probability mass function (pmf) Px(x) = q*p, x = 0,1, 2, .. 0< p< 1, where q- 1-p i) Find P(X 2 x) and show that P(X S3) = 1- q*. ii) Explain why P[X is odd(= 1,3,5,7, ..)] = q x P[X is even(=0,2,4,6, .)) And hence otherwise show that P(X is odd) = +9 iii) Find P(X is od d|X S 3) as a function of q, and, given that D.R EGALA STAT 203 March 4, 2021 Find P(X is odd|X 53) = deduce the value of q. 1 6 he continuous random variable has probability density function (pdf) fx(x) = -20 how that the cumu lative distribution function (edf) of X is 0 +x Fy (x) = 20 - 0 Sx S0 educe an expression for P(X > x). 17 he random variable X has the binomial distribution with probability mass function P(X = X) = (-) p*(1 – p)- , x = 0, 1,2; 0

A 5 The random variable X has the geometric distribution with probability mass function (pmf) Px(x) = qp, x = 0,1, 2, .. 0< p< 1, where q- 1-p i) Find P(X 2 x) and show that P(X S3) = 1- q. ii) Explain why P[X is odd(= 1,3,5,7, ..)] = q x P[X is even(=0,2,4,6, .)) And hence otherwise show that P(X is odd) = +9 iii) Find P(X is od d|X S 3) as a function of q, and, given that D.R EGALA STAT 203 March 4, 2021 Find P(X is odd|X 53) = deduce the value of q. 1 6 he continuous random variable has probability density function (pdf) fx(x) = -20 how that the cumu lative distribution function (edf) of X is 0 +x Fy (x) = 20 - 0 Sx S0 educe an expression for P(X > x). 17 he random variable X has the binomial distribution with probability mass function P(X = X) = (-) p*(1 – p)- , x = 0, 1,2; 0

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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Concept explainers

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!

Question

The random variable X has the geometric distribution with probability mass function (pmf)
Py(x) = q*p. x = 0,1, 2, ... 0 <p< 1,
where q = 1-p
i)
Find P(X 2 x) and show that P(X <3) = 1- q*.
ii)
Explain why
P[X is odd(= 1,3,5,7, .)) = qx P[X is even(= 0,2,4,6, .)]
And hence otherwise show that
P(X is odd) =ta
%3D
iii)
Find P(X is od d|X S 3) as a function of q, and, given that
R.D.R EGALA
STAT 203
March 4, 2021
Find P(X is odd|X < 3) =
deduce the value of q
|A6
The continuous random variable X has probability density function (pdf)
fx (x) =
26
Show that the cumulative distribution function (cdf) of X is
e +x
Fx (x) =
20
Deduce an expression for P(X >x).
|A7
The random variable X has the binomial distribution with probability mass function
() p*(1 - p)²-*,
x = 0, 1,2; 0<p<1.
P(X = X) =
i)
Write down E(X), Var(X) and P(X = 2) in terms of parameter p
ii)
Find ;
a) P(X = 0|X < 2)
b) P(X = 1|X < 2), simplifying your answer as far as possible.

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