Let M be a geometric random variable with parameter p and let X be an exponential
random variable with parameter A.
(a) Compute the tail probabilities P(M > k) and P(X > 1) for the geometric and the
exponential random variable where k is a positive integer and 2 is a non-negative
real number
(b) Plot P(M > k) as a function of k and P(X > 1) as a function of t. Use p= 0.6
and X = 1. Compare the two plots.
(c) A continuous random variable X is said to satisfy the memoryless property if for
all t, h > 0.P(X > 1+h| X > 1) = P(X > h). Prove that the exponential random
variable satisfies the memoryless property.
Answers
Answer:
Draw flowcharts for the following:
1. To accept the length of two line segments and check whether they are equal
or unequal. Display the message accordingly.
2. To enter two angles and check whether they are complementary or not.
3. To enter the age of a person and check whether he/she is eligible to vote or
not.
4. To accept the age of a student and check whether he/she is a teenager or not.
Draw flowcharts for the following:
1. To accept the length of two line segments and check whether they are equal
or unequal. Display the message accordingly.
2. To enter two angles and check whether they are complementary or not.
3. To enter the age of a person and check whether he/she is eligible to vote or
not.
4. To accept the age of a student and check whether he/she is a teenager or not.
Draw flowcharts for the following:
1. To accept the length of two line segments and check whether they are equal
or unequal. Display the message accordingly.
2. To enter two angles and check whether they are complementary or not.
3. To enter the age of a person and check whether he/she is eligible to vote or
not.
4. To accept the age of a student and check whether he/she is a teenager or not.
Draw flowcharts for the following:
1. To accept the length of two line segments and check whether they are equal
or unequal. Display the message accordingly.
2. To enter two angles and check whether they are complementary or not.
3. To enter the age of a person and check whether he/she is eligible to vote or
not.
4. To accept the age of a student and check whether he/she is a teenager or not.
Draw flowcharts for the following:
1. To accept the length of two line segments and check whether they are equal
or unequal. Display the message accordingly.
2. To enter two angles and check whether they are complementary or not.
3. To enter the age of a person and check whether he/she is eligible to vote or
not.
4. To accept the age of a student and check whether he/she is a teenager or not.
Draw flowcharts for the following:
1. To accept the length of two line segments and check whether they are equal
or unequal. Display the message accordingly.
2. To enter two angles and check whether they are complementary or not.
3. To enter the age of a person and check whether he/she is eligible to vote or
not.
4. To accept the age of a student and check whether he/she is a teenager or not.
Answer:
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