Question

Given that p(x) = K/2x us a probability distribution
for a random voorable that can take on the values
x=0, 1,2,3 and 4 i) Determine k Determine mean and variance of x
​

Answer 1

Step-by-step explanation:

p(x)=kx/2

p(0)=0

p(1)=1×k/2 = k/2

p(2)=2×k/2=2k/2

p(3)=3×k/2=3k/2

p(4)=4×k/2=4k/2

we know that sum of probabilities of all outcomes =1

=> 0+k/2+2k/2+3k/2+4k/2=1

1/2×(k+2k+3k+4k)=1

10k=2

k =0.2

p(0)=0

p(1)=0.2/2=0.1

p(2)=0.2×2/2=0.2

p(3)=0.2×3/2=0.3

p(4)=0.2×4/2=0.4

E(x)=sum(x×p(x))= 0×1+1×0.1+2×0.2+3×0.3+4×0.4

= 0+0.1+0.4+0.9+1.6=3

variance =E(x^2)-E(x)^2

E(x^2)=sum (x^2×p)=( 0^2×0.1)+(1^2×.1)+(2^2×.2)+(3^2×.3)+ (4^2×.4)

=0+.1+0.8+2.7+6.4=10

variance =10-(3^2)=10-9=1

mean =3

k=0.2

hope this helps