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I'm currently working on some statistics homework, and as you might guess from the title, I got the wrong result, and the reason why I'm writing it here is because I don't have a clue why it's wrong.

The question is as follows:

A student is driving from city A to B. On route to B there's 2 intersections where she will randomly choose which one to pass through.

1. At the first intersection she can choose between Bridge A or B in the proportion 3:1 (Meaning bridge A is chosen with probability 3/4).

At bridge A there's a 0.5 probability of being delayed by 0 mins. and a 0.5 probability of being delayed by 10mins.

At bridge B there's a 0.4 probability of being delayed by 5mins. and a 0.6 probability of being delayed by 7mins.

2. At the second intersection she can choose between road A or B in the proportion 2:1.

At road A there's a 0.5 probability of being delayed by 1min. and a 0.5 probability of being delayed by 2 mins.

At road B there's a 0.1 probability of being delayed by 3mins. and a 0.9 probability of being delayed by 9mins.

Out from this answer the following:

  1. Let X be a stochastic variable which shows the student's total delay in minutes between city A to B. Calculate the following: $S_x$, $E(X)$, $Var(X)$ and $\sigma_X$

Let's just take the calculation for $S_X$ since I find that one to be the hardest.

Since X is stochastic I can find that it has the following values: 1, 2, 3, 6, 7, 8, 8, 9, 10, 11, 12, 13, 14, 16, 19

In order to calculate $S_x$ I have to calculate the expected value which I did as:

E(X)=$\frac{(1+2+3+6+7+8+8+9+10+11+12+13+14+16+19)}{15} = 9.2667$

Then I believe I calculate $S_X$ the following way:

$S_X$ = $\sqrt(\frac{E(X)}{N})$ = 4.8634

Unless I'm using the wrong method (which I most likely am), then there's something missing in my book because what my teacher calls $S_X$ "Support". Which I can find nothing about, I also tried to look up standard deviation, which also turned out to be wrong.

guntbert
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Nikolaj Kyed
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  • Is Sx somekind of sample variance. I am reasonably good in Statistics but this beats me. I know of no statistic called $S_x$ = $\sqrt{\frac{E(x)}{N}}$. and the calculation that I you laid out is also wrong (is not equal to 4.8634. – Satish Ramanathan Mar 01 '14 at 22:37
  • You are saying it is stochastic and yet you have calculated everything discrete without any assignment of probability. – Satish Ramanathan Mar 01 '14 at 22:39
  • You just used the word discrete which made me thing. I have some shortened notes where it says how to calculate the mean value for a discrete or continuous distribution. Then just below that it says how to calculate variance for a stochastic, discrete and continuous distribution. I'm going to try to calculate it again and then I'll write back to you again. – Nikolaj Kyed Mar 01 '14 at 22:51

2 Answers2

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Answer:

enter image description here

This is the way I would about be calculating EXPECTED VALUE, VARIANCE and STANDARD DEVIATION. I am really not sure about the Sx, whatever you call Support

Satish Ramanathan
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  • Your calculations for E(X), Var(X) and SD(X) are indeed correct. I still haven't been able to figure out Sx yet. – Nikolaj Kyed Mar 01 '14 at 23:06
  • I honestly do not know what Sx means except in some cases the notation is used for Sample Standard Deviation. – Satish Ramanathan Mar 01 '14 at 23:08
  • I might've missed it since I missed one or two lectures, so I will look through the power points from those two days. I will let you know if I find something. And thank you. – Nikolaj Kyed Mar 01 '14 at 23:10
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You can also create a joint probability mass function like the one below and compute E(x), Var(X) and sigma. It turned out that both the methods yielded the same. Just to give you another way to solve it.

enter image description here

Satish Ramanathan
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