Let xn = x2 1 + + x2 n, where the xi's are iid standard normal random variables.

(a) show that sn is a chi-square random variable with n de- grees of freedom.

hint: show that x2 i is chi-square with one degree of freedom, and then use problem 6.

(b) find the pdf of tn = (x2 1 + + x2 n)1=2

(c) show that t2 is a rayleigh random variable.

(d) find the pdf for t3. the random variable t3 is used to model the speed of molecules in a gas. it is said to have the maxwell distribution.

y < -3

step-by-step explanation:

-3y - 2 > 7

-3y -2 + 2 > 7+2

-3y > 9

-3y/-3 < 9/-3   (change the inequality sign when multiplying or dividing by a negative number)

y < -3

true

step-by-step explanation:

intersecting chords are just lines that intersect. so a line is equal to 180 degrees, so when it is intersected by another chord, then it create supplementary angles, and because the lines cross, vertical angels are also formed.

option (a)

step-by-step explanation:

step 1:   take 2 number whose product equal to 25..

and sum of those two number are -10

step: 2 for example here if we take 5,5 are the number,,

5*5=25

and

5+5=10

but we need -10

so if we take   -5,-5

so -5*-5=25

and -5+(-5)=-10

s0

come the equation

replace -10x by these number

like -5x -5x+25

take common

x(x-5)-5(x-5)=0

(x-5)(x-5)=0