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Emmanuel S.

Probability

2 months, 1 week ago

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Hi am david and i'm here to have your answering your question in the question here we are going to discuss about the probability mass function here. We are given the a b c, so let me do 1 by 1 for the question for a. We are given that the b x equal to the c times 3 to 5 power x and for the x it will equal to the 135 and so on, and i need to find the value of the c. We know that it will sum over the p x for own x and the son was equal to the 1 and therefore we get equal to the summation. I'M the c will be a constant, then 3 over 5 and the power of the x and then for x. It will be equal to the 1 for own x here. So t means that we have the c constant i can bring outside the first x. It can be the 1, so we met the 3 over 5 power 1 then x, equal to the 3. Then we have the 3 over 5 pour 3 plus the 3 over 5 power, 5 plus 3 or 5 power of the 7 and so on. And then we can write this down as a c there's going to be the summation of the 3 over 5. This 1 will be. I can call this 1 will be the 2 k plus 1 and the k it will be equal to starting from the 0 up to the infinity and then from here. We can simplify this 1. By doing this, 1 will be the summation. I can write it as the 3 out of 5 times and the 3 out of 5 square and then to the k and then k go from 0 to infinity, and then we have the c, and now we will have it equal to this. 1 will be a constant it can bring outside. They will have the 3 c over 5 and then submission okay go from 0 up to infinity, and this i have the 3 out of 5 that will be the square, so we get equal to the 9 out of 25 power k, and we know that this Submission here is equal to the geometric series, therefore equal to 1 over 1 minus 9 over 25 point, and if you compute him the 3 c over 5 times worth now. We have the 25 dividing by here, twentyfive minus 9, equal to the 16 point, and if we simplify it, we will have 5 times. 3 will be the 15 c out of the 16 point. We want to be equal to the 1. Therefore, we want to equal to the 16 over the 15 and that's going to be the answer for the question 1 and then for the question for b. I we are given that the b x equal to the c times of the x plus 1 square for the x equal to 012 and 3. Only therefore, we have 1 was equal to the summation of the b x, which equal to the cousin and for the x equal to the 0 were conal into the formula we have. The 0 plus 1 will be, the 1 square will be 1, and when we have the 1 inside, we have, the 2 square will be the 4 for the x equal to the 2. An the 3 square would be the 9 for the 3 equal to the 4 square will be the 16 point then equal to here we have the 10 and then 20 will be the 30 c and therefore the c here equal to the 1 over the 30 Point- and that will be the answer for the 4 b and for the first c we are given the p x equal to the x o c, for the x equals to 1. Up to the non again, we will have. The 1 was equal to the summation gone peal to 1 over c, which a constant i can bring outside the number 1 plus 2 plus 3, plus up to the n, and this 1 go to the 1 over this summation by the formula equals to n times. N plus 1 divided by 2, and this only equal to the c. Therefore, the c is equal to the time n plus 1 divded by 2, and that's gonna be the answer for your question.

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