toss two coins let x be the resulting number of heads and y be the number of tails find the distribution in R

Question

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Answer 1

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Answer 2

The distribution of x and y when tossing two coins can be modeled as a discrete uniform distribution with parameters n=2 (number of coins) and k=2 (number of possible outcomes, heads or tails). The possible values of x and y are (0,2), (1,1), and (2,0), with equal probabilities of 1/3 each. The distribution in R can be represented as: P(x=0)=P(y=2)=1/3, P(x=1)=P(y=1)=1/3, and P(x=2)=P(y=0)=1/3.

When tossing two coins, each coin has two possible outcomes: heads (H) or tails (T). The total number of possible outcomes when tossing two coins is 2^2 = 4, namely (H,H), (H,T), (T,H), and (T,T). The number of heads (x) and the number of tails (y) are related by x + y = 2, where x and y are non-negative integers.

The distribution of x and y can be modeled as a discrete uniform distribution, where each outcome has the same probability. The possible values of x and y are (0,2), (1,1), and (2,0), with equal probabilities of 1/3 each. This means that the probability of getting 0 heads and 2 tails is 1/3, the probability of getting 1 head and 1 tail is 1/3, and the probability of getting 2 heads and 0 tails is 1/3.

In mathematical terms, the distribution in R can be represented as: P(x=0)=P(y=2)=1/3, P(x=1)=P(y=1)=1/3, and P(x=2)=P(y=0)=1/3. This represents the probability of x and y taking on each of the three possible values.