Probability and Statistics - Online Test

TOTAL NO. OF OUTCOMES=62=36

no. of outcomes in which both throws same no.={(1,1),(2,2),(3,3),(4,4),(5,5),(6,6)}=6

p(both throws same no.)=6/36=1/6

let us assume that y = 3x – 5 and y = 2x – 4 are lines of regression of x on y and y on x respectively,therefore

bxy=1/3byx=2

ρ=±bxybyx−−−−−√=±2/3−−−√

but sign of ρ$\rho$ is same as byx and bxy

therefore ρ=2/3−−−√

Total number of ways of getting even number is 3

Out of these 3 even number we have to get either 2 or 4 which can be done in 2 ways.

So required probability is 2/3

on tossing a pair of  dice total outcomes are 36

out of which getting a total of 8 have possiblities {(2,6),(6,2),(3,5),(5,3),(4,4)}=5

and from these 5 outcomes getting same no. on both dice is (4,4)=1

so, probability is 1/5

We know that, 3median = mode + 2 mean

so, mean= (3 median - mode)/2      ........(1)

comparing equation(1) with the given equation

therefore, x=1/2