Question

suppose a random variable, x, arises from a binomial experiment. write the probability distribution. round to six decimal places, if neces x p(x) 0 0.282430 1 2 3 4 5 0.001203 6 0.000047 select the correct histogram.

Explanation:

1. Recall the binomial probability formula:

• The binomial probability formula is \(P(x)=C(n,x)\times p^{x}\times(1 - p)^{n - x}\), where \(C(n,x)=\frac{n!}{x!(n - x)!}\), \(n\) is the number of trials, \(x\) is the number of successes, \(p\) is the probability of success on a single - trial, and \(1-p\) is the probability of failure on a single trial. However, since we are not given \(n\) and \(p\) values, and we already have some of the probabilities filled in the table, we assume we are just completing the table based on the given values and the properties of a probability distribution.
• We know that for a discrete probability distribution \(\sum_{x = 0}^{n}P(x)=1\). Let's assume the values of \(P(0) = 0.282430\), \(P(5)=0.001203\), and \(P(6)=0.000047\).

1. Calculate the sum of the known probabilities:

• Let \(S=P(0)+P(5)+P(6)=0.282430 + 0.001203+0.000047=0.28368\).

1. Assume the remaining probabilities \(P(1)\), \(P(2)\), \(P(3)\), and \(P(4)\) are such that \(\sum_{x = 0}^{6}P(x)=1\). But without more information about the binomial parameters \(n\) and \(p\), if we assume the distribution is complete with just these non - zero probabilities at \(x = 0\), \(x = 5\), and \(x = 6\), then \(P(1)=0\), \(P(2)=0\), \(P(3)=0\), \(P(4)=0\).

• The probability distribution table is:

\(x\)	\(P(x)\)
1	0
2	0
3	0
4	0
5	0.001203
6	0.000047

Answer:

\(x\)	\(P(x)\)
1	0
2	0
3	0
4	0
5	0.001203
6	0.000047