determine the following attached with formulas to assist Question # 1The disczete zandom variable X has probability mas function given by(4)"P(X -x) -kx-123.4,5x-6where k is a constantotherwise(4) Determine the valne of k(b) Find the mode(e) Find the mean and variance of the distribution Statistics FormulaeΣΑMean. με ΣSample Variance = s.Some Probability FormulaeP(AUB) = P(A) + P(B)- P(AOB)1.PANB); P(B)>02.P(A B) =PB)3.P(AnB) = P(A/ B)+ P(B)4.P(AIB) = P(A)P(AnB) = P(A) • P(B)5.P(A) = PA/ B)B) + PA/B)P(P(B)6.P(BI A)P(A)8.P(A B) =PBI A)P(A) + PMBIA)PA)με ΕίX) Σα)9.a =V(X) = E[(X - ']=E(x-' P(x)10.a =V(X) = E(X) -[E(X)r11.n!12.P(x) =13.= np: o= npqPlx) = 'e".14.for x= 0,1,2,3.15.P(x)=pqx-

a) To find the value of k, use the condition of valid pdf…

The disczete zandom variable X has probablity mass function given by (4)" P(X -x) -k x-12345 x-6 where k is a constant otherwise (4) Detecmine the value of k (6) Find the mode (e) Find the mean and vasiance of the distzībution

The disczete zandom variable X has probablity mass function given by (4)" P(X -x) -k x-12345 x-6 where k is a constant otherwise (4) Detecmine the value of k (6) Find the mode (e) Find the mean and vasiance of the distzībution

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Concept explainers

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

Question

determine the following attached with formulas to assist

Statistics Formulae
ΣΑ
Mean. με Σ
Sample Variance = s.
Some Probability Formulae
P(AUB) = P(A) + P(B)- P(AOB)
1.
PANB)
; P(B)>0
2.
P(A B) =
PB)
3.
P(AnB) = P(A/ B)+ P(B)
4.
P(AIB) = P(A)
P(AnB) = P(A) • P(B)
5.
P(A) = PA/ B)B) + PA/B)P(P(B)
6.
P(BI A)P(A)
8.
P(A B) =
PBI A)P(A) + PMBIA)PA)
με ΕίX) Σα)
9.
a =V(X) = E[(X - ']=E(x-' P(x)
10.
a =V(X) = E(X) -[E(X)r
11.
n!
12.
P(x) =
13.
= np: o
= npq
Plx) = 'e".
14.
for x= 0,1,2,3.
15.
P(x)=pqx-

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