A binomial random variable is based on n = 28 and p = 0.7. Find x2P(x). (Give your answer correct to two decimal places.)
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To find x2P(x), we need to calculate the product of x² and the probability of x.
In a binomial distribution, the random variable x represents the number of successful outcomes, n is the number of trials, and p is the probability of success in each trial.
Given that n = 28 and p = 0.7, we can find x²P(x) by following these steps:
Step 1: Determine the values x can take.
Since the question does not specify the value of x, we need to consider all possible values of x that the binomial random variable can take. The range of x will be from 0 to n (28 in this case).
Step 2: Calculate P(x) for each value of x.
To calculate P(x), we use the binomial probability formula: P(x) = nCx * p^x * (1-p)^(n-x), where nCx represents the number of combinations of n items taken x at a time.
Step 3: Calculate x²P(x) for each value of x.
For each value of x, we find the product of x² and P(x): x²P(x) = x² * P(x).
Step 4: Sum up all the x²P(x) values.
Finally, we add up all the calculated x²P(x) values to get the overall value of x²P(x).
Given that n = 28 and p = 0.7, you would need to calculate x²P(x) for all the possible values of x (from 0 to 28) and sum up those values.