 # Probability distribution of random variable (PROPORTION OF DIAMOND KINGS IN A SAMPLE - Week 18)

I have calculated PMF of proportion of diamond kings as
P(K == 0) = (3/4)^4
P(K == 1) = (3/4)^3 * (1/4)
P(K == 2) = (3/4)^2 * (1/4)^2
P(K == 3) = (3/4) * (1/4)^3
P(K == 4) =(1/4)^4
Which is decreasing

But in the video it is right skewed normal
can you please explain Probability mass function(PMF)

Let’s just only consider the case for K=0, i.e. none of the 4 groups of 13 cards in the sample contains a diamond king.

Population Size, N = \binom{52}{13},
Out of these N, number of elements(group of 13) with no Diamond King M= \binom{51}{13}

Total ways to draw sample of size 4, n = \binom{N}{4}
Total ways to draw sample of size 4 with no element containing diamond king = \binom{M}{4}

Probability of proportion of samples with no element containing diamond King: P(K=0) = \binom{M}{4}/\binom{N}{4}

So I think, the calculation might be a bit different. (Calculation above is just my understanding, you can verify)
If you agree with above, you can calculate for K=1,2,3,4 and check the skewness.

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Can you help me understand how you arrived at figures ¾ and ¼ in your calculations.

How can probability of not having diamond king in a sample of 13 cards be ¾ ?

Regards

Subbu