ONLY ANSWER QUESTION 2.c 2. (4 pts each) Amanda likes to draw pictures with a fr

Question

ONLY ANSWER QUESTION 2.c

2. (4 pts each) Amanda likes to draw pictures with a friend. Amanda tends to draw pictures in one of three themes: dragons, elves, or fairies. If Amanda decides to draw a picture in one theme, her friend is twice as likely to draw a picture of the same theme than to draw a picture in either of the other two themes. If her friend decides to draw something different, she is equally likely to pick either of the remaining two themes (a) Suppose that half the time Amanda draws dragons, 30% of the tine elves, and that she draws fairies only 20% of the time. Calculate the probability of her friend drawing a elf while visiting Suppose Amanda's friend is known to be drawing Legolas (an elf), what are the chances that Amanda is drawing an elf? (b) (c) The time it takes Amanda to draw a dragon is exponentially distributed with a mean of 30 minutes. The time her friend takes to draw a landscape is also distributed, but with a mean of 25 minutes. When one finishes, the other one quits so they can go watch T.V. together. What is the expected amount of time until they are ready to watch T.V.? (d) Amanda draws a set of three pictures. Walking through the room, you notice that one of them is a picture of a dragon. What are the chances that the other two are also dragons? Here assume the choice of theme is independent from picture to picture (e) When you ask about the picture, Amanda tells you it is Smaug from The Hobbit, and that it was first picture she drew that day. Does this new information change the chances that the other two pictures are dragons? If so, exactly how?

Explanation / Answer

The question 2.c doesn't clearly state whether Amanda is indeed drawing a dragon only. If she could be drawing any of the other two themes also, we would need to know the distribution for those as well. Also, we don't know if her friend is indeed drawing a landscape only.

We move forward by assuming that Indeed Amanda is drawing a dragon, her friend is drawing a landscape and that they both start at the same time. In that case,

Time to watch TV= Min ( E(Amanda), E(Friend))

Where E(Amanda)= Expected value of time taken by Amanda to complete her drawing

and E(Friend)= Expected value of time taken by the friend to complete her drawing

Expected value of exponential distibution= Mean

Thus, E(Amanda)= 30 Min

E(Friend)= 25 Min

and time to watch TV= Min( 30, 25)= 25 minutes

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