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1. A biased coin has probability 0.4 of showing a head. In an experiment, the coin is spun
until a head appears. If a head has not appeared after 4 spins, the coin is not spun again. The random variable X represents the number of times the coin is spun. For example, X = 3 if the first two spins do not show a head but the third spin does show a head. The coin would not then be spun a fourth time since the coin has already shown a head.
(a) Show that P(X = 3) = 0.144
The table gives some values for the probability distribution of X
x = 1 2 3 4
P(X = x)= 0.24 0.144
(b) (i) Write down the value of P(X = 1) (ii) Find P(X = 4)
(c) Find E(X ) (2) (d) Find Var(X )
The random variable H represents the number of heads obtained when the coin is spun in the experiment.
(e) Explain why H can only take the values 0 and 1 and find the probability distribution of H.
(f) Write down the value of
(i) P({X = 3} ∩ {H = 0})
(ii) P({X = 4} ∩ {H = 0})
The random variable S = X + H
(g) Find the probability distribution of S
2. working out..?
working out..?
i dont know how to continue from part -e-
4. H means that when you spin a coin how many heads to you get:
• If you spin the coin and land on tails then H=0
• If you spin the coin and land on heads then H=0

p(H=0)=p(land on a tail)
5. (Original post by lili4648)
H means that when you spin a coin how many heads to you get:
• If you spin the coin and land on tails then H=0
• If you spin the coin and land on heads then H=0

p(H=0)=p(land on a tail)
yes and part -f- ?

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