Question

suppose that a four-sided die has faces marked 1,2,3 and 4. Toss the die once. let X be the outcome of the random process.

a)what the probability distribution for X
b)find the expected value of X
c)find the standard deviation of X

Answer 1

x = Osteome of our team ane Bauale likely) x = Outcome of tossing a die (4-sided) once 4 x= 1, 2, 3, 4 (each 4 faces are aqualy likely) ay PMF of X : P(x=2) = { 1 , x=1,2,3,4 ló ele 1 x. Discrete Uniform (1,4) 5) E(x) = {z P(x=z) - , *(1+2+3+4)= 102 - 12-5] (Ezpeted azlue) c) E(X2)= Ž Px-2) 3 = (**2+3+4)= 30 = 7.5 .: Var (x) = E(X2)- (X)= 7.5 - (2-5) = 1.25 .: Standard deviation - Vax(x) = {1-118033 Z =1