another s1 question.. binomial distribution

.x.g.x.

1

hi sorry, can someone give me abit of help of this question..

a) the random variable W has a B(6, 0.4) distribution. calculate the probability that the value of W is an odd number.

i made a p.d.f but when i added them up it didnt = 1, sumthing like 0.95..
???

b) the random variable X has a B(5, p) distribution, where p ≠ 0. given that E(X) = 3Var(X), find P(X=0)

c) the random variable Y has a B(12,p) distribution where p ≠ 0. given that
P(Y=11) = P(Y=12) find the vaule of p

if any1 can give me any hints or something then thankyou!

Reply 1

Dekota

.x.g.x.

c) the random variable Y has a B(12,p) distribution where p ≠ 0. given that
P(Y=11) = P(Y=12) find the vaule of p

P(Y = 11) = 12C11.(p)^11.(1-p)
P(Y = 12) = 12C12.(p)^12

P(Y = 11) = 12(p)^11.(1-p)
P(Y = 12) = (p)^12

(p)^12 = 12(p)^11.(1-p)
(p)^12 = 12(p)^11 - 12(p)^12
0 = 12(p)^11 - 13(p)^12
0 = 12/13p^11 - p^12
0 = p^11(12/13 - p)
0 = 12/13 - p

p = 12/13
--------------

.x.g.x.

hi sorry, can someone give me abit of help of this question..

a) the random variable W has a B(6, 0.4) distribution. calculate the probability that the value of W is an odd number.

i made a p.d.f but when i added them up it didnt = 1, sumthing like 0.95..
???

Hehe! What is a p.d.f? :redface:

I haven't done further stats ...

Reply 2

.x.g.x.

OP

1

thanks, do u know how to do a & b?

Reply 3

Jonny W

8

(a)
P(W = 1) + P(W = 3) + P(W = 5)
= 6C1 (0.4)(0.6)^5 + 6C3 (0.4)^3(0.6)^3 + 6C5 (0.4)^5(0.6)
= 0.500

(b)
E(X) = 5p
Var(X) = 5p(1 - p)

Since E(X) = 3Var(X),

5p = 15p(1 - p)
p = 3p(1 - p)
p = 3p - 3p^2
3p^2 - 2p = 0
p(3p - 2) = 0
p = 2/3 . . . . . since p $\neq$ 0

P(X = 0)
= (1/3)^5
= 0.004

(c)
P(Y = 11)
= 12C11 p^11 (1 - p)
= 12 p^11 (1 - p)

P(Y = 12) = p^12

p^12 = 12 p^11 (1 - p)
p^11(p - 12(1 - p)) = 0
p^11(13p - 12) = 0
p = 12/13 . . . . . since p $\neq$ 0

Reply 4

.x.g.x.

OP

1

its not further stats, its in s1 for ocr, its the table you draw out

W 1 2 3 4 5 6
p(W=w)

looks 'abit' like that?!

Reply 5

Dekota

.x.g.x.

its not further stats, its in s1 for ocr, its the table you draw out

W 1 2 3 4 5 6
p(W=w)

looks 'abit' like that?!

Cheers!

Reply 6

.x.g.x.

OP

1

thankyou!!
i sat there for ages tryin to do that question and now i see the working its so easy!! i'm like.. why didnt i think of that!?
--------------

Dekota

Cheers!

lol sorry cant explain it

another s1 question.. binomial distribution

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