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# Joint and marginal probability mass functions in coin toss

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A fair coin is tossed four times and X is number of heads on first three tosses and Y on last three. What is the joint probability mass function of x and y? What is the marginal pmf? Are X and Y independent?

https://brainmass.com/statistics/probability-density-function/joint-and-marginal-probability-mass-functions-in-coin-toss-277664

#### Solution Preview

A fair coin is tossed four times and X is number of heads on first three tosses and Y on last three. What is the joint probability mass function of x and y? What is the marginal pmf? Are X and Y independent?

The joint mass function can be calculated as follows.

The chance of heads in a toss = 0.5

The chance of k heads in first 3 tosses = C(3, k) x 0.5^3

where C(3, k) means 3 choose k = 3!/[k!(3-k)!] where ! means factorial.

If k = 0,

Probability(X = 0, Y ...

#### Solution Summary

How to calculate the joint probability density function of non-independent events in a coin toss?

How to calculate marginal density function from joint density function?

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