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.

Part A
(26)x = 1
divide both sides by 26
(26)x/26 = 1/26
cancel out the 26 above n below
x = 1/26

Part B
(50)x = 1
divide both sides by 50
(50)x/50 = 1/50
cancel out the 50 above n below
x = 1/50

Not sure why there are other possible value of x...plz double-check ur prob.

Edit: (2^6)x = 1

since 2^6 = 2*2*2*2*2*2 = 64

64x = 1

x = 1/64

(5^0)x = 1

as any number raises to the zero power =1

x = 1

still don't see how there are other possible numbers lol