- #1
Jessica21
- 5
- 0
1. A necklace consists of 5 beads on a string. The beads for making the necklace are drawn at random from a box containing a very large number of beads. 2/3 of the beads are pink and 1/3 are blue. find the mean and variance of the number of unlike pairs of adjacent beads in the necklace.
I am having trouble understanding what they mean by " the number of unlike pairs of adjacent beads"
2. well i know mean = E(x) = sum of all x of xf(x)
and Var (x)= E[(X-mean)^2]
3. attempt: so if i number the beads that go in the necklace from 1 to 5.
let X1 = 1 if beads 1 and 2 are different , and X1 = 0 if they are the same.
let X2 = 1 if beads 2 and 3 are different, and X2 = 0 if they are the same.
...
let X5 = 1 if beads 5 and 1 are different , and X5 = 0 if they are the same.
but i don't know how to find the probability function.
I am having trouble understanding what they mean by " the number of unlike pairs of adjacent beads"
2. well i know mean = E(x) = sum of all x of xf(x)
and Var (x)= E[(X-mean)^2]
3. attempt: so if i number the beads that go in the necklace from 1 to 5.
let X1 = 1 if beads 1 and 2 are different , and X1 = 0 if they are the same.
let X2 = 1 if beads 2 and 3 are different, and X2 = 0 if they are the same.
...
let X5 = 1 if beads 5 and 1 are different , and X5 = 0 if they are the same.
but i don't know how to find the probability function.