A random variable X has the distribution functionx: 0 1 2 3 4 5 6 7P(x): 0 k 2k 2k 3k2k22kkk 27Then evaluate)

Question

A random variable X has the distribution function

x:     0   1   2   3   4   5   6   7
P(x):  0   k   2k  2k  3k  2k  2k  2k + 27

Then evaluate)

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Solution

It seems like there's a formatting issue with your question, making it difficult to understand. However, I can tell you that if X is a random variable with a given distribution, the sum of all probabilities in that distribution should equal 1.

If we denote the probabilities as follows:

P(X=0) = 0 P(X=1) = k P(X=2) = 2k P(X=3) = 2k P(X=4) = 3k P(X=5) = 2k P(X=6) = 2k P(X=7) = k

Then, the sum of these probabilities should be 1, i.e.,

0 + k + 2k + 2k + 3k + 2k + 2k + k = 1 12k = 1 k = 1/12

Please check your question and provide the correct distribution if this is not what you were asking.

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A random variable X has the distribution functionx: 0 1 2 3 4 5 6 7P(x): 0 k 2k 2k 3k2k22kkk 27Then evaluate)

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