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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?

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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?

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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Statistics: Joint probabilty with coins and die

A die is rolled and the number observed X is recorded. Then a coin is tossed number of times equal to the value of X . For example if X = 2 then the coin is tossed twice, etc. Let Y be the number of heads observed.

Note: Assume that the die and the coin are fair. What is the joint probability mass function of X and Y? What is the marginal probability mass function of X and Y?

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