Find probability function and E(X)A bowl contains six marbles of which two are green and four are red. The marbles are removed one by one, at random and without replacement. Let X be the number of the drawing at which a red marble is removed for the first time. Find the probability function of X, and E ( X ).For the probability function, I believe that this question is a geometric distribution, so I have P [ X = x ] = p q x − 1 For E ( X ) = 1 / p since it's geometric distributionIs it the Hypergeometric distribution?So E ( Y ) = n r / N

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Find probability function and E(X)A bowl contains six marbles of which two are green and four are red. The marbles are removed one by one, at random and without replacement. Let X be the number of the drawing at which a red marble is removed for the first time. Find the probability function of X, and       E    (  X  ).For the probability function, I believe that this question is a geometric distribution, so I have       P    [  X  =  x  ]  =  p      q          x      −      1      For       E    (  X  )  =  1      /    p since it&#039;s geometric distributionIs it the Hypergeometric distribution?So   E  (  Y  )  =  n  r      /    N

suponeriq · Accepted Answer

Step 1No, you are not correct; for a geometric distribution, you have to have the same probability of &quot;success&quot; on each draw, whereas here the probability of getting a red depends on the marbles that have been drawn so far.Step 2For instance: the probability that you first get a red marble on the second draw is precisely the probability of getting a green first and then a red, which is       2    6    ⋅      4    5

A bowl contains six marbles of which two are green and four are red. The marbles are removed one by one, at random and without replacement. Let X be the number of the drawing at which a red marble is removed for the first time. Find the probability function of X, and E(X)

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