Three tables listed below show random variables and their...

Three tables listed below show random variables and their probabilities. However, only one of these is actually a probability distribution. A B C x P(x) x P(x) x P(x) 25 0.4 25 0.4 25 0.4 50 0.1 50 0.1 50 0.1 75 0.3 75 0.3 75 0.3 100 0.4 100 0.2 100 0.6 a. Which of the above tables is a probability distribution? B b. Using the correct probability distribution, find the probability that x is: 1. Exactly 25 = 2. No more than 50 = 3. More than 25 =

Transcript

00:01 Hello everyone we are going to solve a question and in this question we are given this data these three tables ab and c and we are asked that which of them is probability distribution for a part for probability distribution the summation of probability must be equals to 1 so when we solve add up these here we get 1 when we add up these here we get 1 in 3 4 4 and 4 8 and 12 that is 1 .2 and here we get for 1 .4 so as this is greater than 1 that not equal to 1 this summation is also not equal to 1 so that means a is probability distribution out of them a is probability distribution so this is the answer for a part now moving on to the b part in b part we have three questions in b part first one is we have to find probability when x is equals to 15 so from this table this is equals to 0 .4 so this is the answer for first question the second one is we have to find the probability such that x is less than equals to 10 so this is equal to probability when x is 5 and probability when x is 10 from this table now from the table we put the values this is equals to 0 .1 plus 0 .3.

01:30 So this is equals to 0 .4 which is the answer for this question.

01:35 Now moving on to the third question, it is probability when x is greater than 5.

01:40 So this is equals to when 1 minus probability x is less than equals to 5.

01:45 So in this table this is equals to 1 minus probability of x equals to 5 as there is no term less than 5.

01:53 So this is equals to 1 minus 0 .1 so this is 0 .9 so hence this is the answer for this third part now i'm moving on to the c part in c part we have to find in first part mean so mean is denoted by mu which is equals to x this is equals to summation x multiplied with p x so on solving this is equals to 5 multiplied with 0 .1 plus 10 multiplied with 0 .3 plus 15 multiplied with 0 .4 and plus 20 multiplied with 0 .2 then this is equals to on solving we get 13 .5.

02:35 So hence mean is equals to 13 .5.

02:40 Now in second part we have to find variance.

02:44 In second part we have to find variance that is sigma square.

02:49 So this is equals to ex square minus ex whole.

02:54 Square...

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