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9966 [12]
3 years ago
5

An ordinary (fair) coin is tossed 3 times. Outcomes are thus triples of "heads" (An ordinary (fair) coin is tossed 3 times. Ou)

and "tails" () which we write , , etc. For each outcome, let be the random variable counting the number of tails in each outcome. For example, if the outcome is , then . Suppose that the random variable is defined in terms of as follows: . The values of are thus:Outcome Value of Calculate the probability distribution function of , i.e. the function . First, fill in the first row with the values of . Then fill in thevalue x of X Px(X)
Mathematics
1 answer:
shepuryov [24]3 years ago
4 0

Answer:

Probability distribution

X    P(X)

0    1/8

1     3/8  

2    3/8

3     1/8

Step-by-step explanation:

When a coin is tossed there are two outcomes head and tail. When three coins are tossed the possible outcomes are

Sample space=S={HTH,THH,TTH,HHH,HTT,THT,TTT,HHT}

The total number of outcomes is n(S)=8. The X be the random variable counting number of tails in each outcome and so X can take values as 0,1,2,3. The probabilities can be computed as P(X)=n(X)/n(S). The probabilities are calculated as under:

X   Outcomes           P(X)

0    HHH                    1/8

1     HHT,THH,HTH    3/8  

2    TTH,HTT,THT     3/8

3    TTT                        1/8

The probability distribution of X is as under:

X    P(X)

0    1/8

1     3/8  

2    3/8

3     1/8

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Answer:

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b) A₂ /A₃  = (r₂²   - r₁²) / (r₃²   - r₂²)

Step-by-step explanation:

We have Circle 1  and area  A₁  

Area of circle 2 outside circle 1     =  A₂

Area of circle 3 outside circle 2    = A₃

On the other hand we have

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A₂´ =  π*r₂² area of circle 2

A₃´ = π*r₃²  area of circle 3

All areas in cm²

a) A₁ /A₂        

A₁  =  π*r₁²

According to problem statement  A₂  = π*r₂²  -   A₁

A₂  =  π*r₂²  -   π*r₁²      ⇒         A₂  =  π* (r₂²   - r₁²)

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b)  A₂ /A₃        

A₂  =   π* (r₂²   - r₁²)

And

A₃   =  π* (r₃²   - r₂²)

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A₂ /A₃  = (r₂²   - r₁²) / (r₃²   - r₂²)

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