Question

A man aiming at a target receives 10 points if his hot is within 1 inch of the target, 5 points if it is between 1 and 3 inches of the target and 3 points if it is between 3 and 5 inches of the target. Find the expected number of points scored if the distance from the shot to the target is uniformly distributed between 0 and 10.

Answer 1

Answer:

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Step-by-step explanation:

hope it helped

Answer 2

Answer:

The answer is 2.6.

Step-by-step explanation:

i) Given data,

Score of 10: within 1 inch of target

Score of 5: within 1-3 inches of target

Score 3: Within 3-5 inches of target

Score of 0: Within 5-10 inches of target

ii) Since the distance from the shot is uniformly distributed,

Probability of score 10 = 1/10

Probability of score 5 = 2/10

Probability of score 3 = 2/10

Probability of score 0 = 5/10

iii) Expected score =∑ $x.P(x)$

= $\frac{1}{10} [10 * 1 + 5*2 + 3*2 + 0*5]$

= $\frac{26}{10}$

= 2.6

iv) Hence, the answer is 2.6.

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