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zmey [24]
3 years ago
7

There are two coins, one with probability p1 of Heads and the other with probability p2 of Heads. One of the coins is randomly c

hosen (with equal probabilities for the two coins). It is then flipped n ≥ 2 times. Let X be the number of times it lands Heads. a) Find the PMF of X. b) What is the distribution of X if p1 = p2?
Mathematics
1 answer:
aivan3 [116]3 years ago
8 0

Answer:

X = 0.5*(p1+p2)*n

a) X = pn

Step-by-step explanation:

Hello!

Since the coin is randomly chosen we can give the probability of choosing one or the other 0.5.

Now, X must be given by the probability of heads for either of the coins, since we do not know which coin have been choosed we must consider both of them, but multiplied by the 0.5 probability to choose one of them.

That is:

X = 0.5*(p1+p2)*n

a) If p1 = p2 = p

X = p*n

which makes sense since is the same as only having one coin

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Answer:

x1 = 275 miles (shorter)

x2 = 318 miles (longer)

Step-by-step explanation:

Let

x1 = be the shorter route

v1 = speed of the car in the shorter route

t1 = time it took to cover shorter route

x2 = the longer route

v2 = speed of the car in the longer route

t2 = time it took to cover longer route


x1 + 43 = x2   (1)

v2 = v1 -2   (2)


v2 = x2/t2 = x2/6

v1 = x1/t1 = x1/5


This means that

v2 = v1 -2   =>

x2/6 = x1/5 -2

The system of equations results

a.   x1 -x2 = -43

b.  x1/5 - x2/6 = 2

Solving this system of equations, we find that

x1 = 275 miles

x2 = 318 miles


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3 years ago
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geniusboy [140]

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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