Four independent flips of a fair coin are made. Let X denote the number of heads obtained. Plot the probability mass function of the random variable X − 2.

Four independent flips of a fair coin are made. Let X denote the number of heads obtained. Plot the probability mass function of the random variable X − 2.

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Four independent flips of a fair coin are made. Let X denote the number of heads obtained. Plot the probability mass function of the random variable X − 2.

Four independent
hansel

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If X denotes the number of heads and we flip a coin 4 times, then the probability mass function X-2 can take on the following values {-2,1,0,1,2}. The probabilities can be found by using the binomial probability formula,

$$P(X)=C(n,k)p^k(1-p)^{n-k}$$

where in this case, k is the number of heads,

for n = 4, and p = 1/2 we have,

$$P(X=-2)=P(\text{0 heads}) = C(4,0)(1/2)^4(1/2)^0=(1/2)^4$$

$$P(X=-1)=P(\text{1 heads}) = C(4,1)(1/2)^3(1/2)^{4-1}=4(1/2)^4$$

proceed in this manner until you have found P(X=0), P(X=1), and P(X=2). And verify the values add up to 1.

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