Question 22 A particular system in a space vehicle has 6...

Question 22 A particular system in a space vehicle has 6 components. The number of components that will be working on Day 7 after the launch of the space vehicle is a random variable Y whose probability mass function is given below: \begin{tabular}{|c|c|c|c|c|} \hline x & 2 & 3 & 4 & 6 \\ \hline P(X=x) & 0.4 & 0.2 & $\theta$ & 0.1 + 2$\theta$ \\ \hline \end{tabular} The percentage confidence coefficient in the system, C is given by C = 10 + 15X. What is the variance of the percentage confidence coefficient C? 639

Transcript

00:01 Here on this problem, we have been given a frequency table, and we've been told that x is the randomly selected shuttle mission between april 1981 and july of 2000.

00:12 Part a asks us to define what are the possible values of the random variable x.

00:17 Well, since x is the crew size, then all the possible values are just the numbers of the crew size.

00:22 And so this means that x is an element of the sample space to...

00:32 Three, four, five, six, seven, and eight.

00:37 And so x can take on any of those given values.

00:43 Now b tells us to use random variable notation to represent the event that the shuttle mission obtained as a crew size of seven.

00:52 Now, random variable notation is in set like this.

00:56 And this would be when x is equal to seven.

01:00 And so this would be the event x equals seven.

01:03 That means you have crew size of seven.

01:09 Now c tells us to find that.

01:11 The probability that x is equal of four.

01:15 Now the probability that x is equal to four is equal to a numerator of two.

01:24 The reason the numerator is two is because there's two times that was the frequency.

01:29 And then for your denominator, do you need to know the total of number of events that happen? and so you add up everything in the frequency row.

01:37 Everything in the frequency row, and there are 96 total events.

01:41 So your probability is 2 over 96.

01:43 And they did want this as a percentage.

01:48 And so we take this and multiply it by 100.

01:56 This gives us 2 .08%.

02:00 So the probability that x is equal to 4 is 2 .08%.

02:09 Now details us to obtain the probability distribution of x.

02:16 Now for the probability distribution of x, let's make a table.

02:27 We said that all the values are 2 through 8...

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