Introduction to probability distribution coin toss:
In probability, a probability distribution used to identify with in a particular interval falling value of a probability. The probability distribution describes the range of the possible value of a random variable. The probability distribution is entirely described by the cumulative distribution function. In this article we shall discuss probability distribution coin toss example problem.
Probability Distribution Coin Toss Example Problem
Example: A coin is tossed for 65times. Find the expectation value of tail with the help of using the binomial distribution.
Solution:
Consider 65 times the coin is tossed, so n = 65
When toss a coin, we get probability of tail is p = 1/2
Probability of getting tail is represent by q
q = 1 – p [p + q = 1]
q = 1 – 1/2
q = 1/2
Expectation value:
μ = E[x] = np
= 65(1/2 )
= (65/2)
μ = E[x] = 32.5
Answer:
Expectation value = μ = E[x] = 32.5
Example 2: An unbiased die is rolling for 45 times. By using the binomial distribution find the expectation value of getting four?
Solution:
Let p be probability of getting success
Let q = 1 – p probability of getting failure
Let n be number of times the dice is thrown
An unbiased dice is rolling for 45 times, the value of n = 43
When we throe a unbiased dice, probability of getting four is p = 1/6
Probability of not getting four is represent by q
q = 1 – p
= 1 – 1/6
= 6/6– 1/6
= 6-1/6
q = 5/6
Expectation value:
μ = E(x) = np
= 45 (1/6)
= 45/6
= 7.5
μ = E(x) = 7.5
Answer:
Expectation value = μ = E[x] = 7.5
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Probability Distribution Coin Toss Practice Problem
Problem:
A coin is tossed for 42 times. Find the expectation value of tail with the help of using the binomial distribution.
Answer:
Expectation value = 21
Problem:
An unbiased die is rolling for 35 times. By using the binomial distribution find the expectation value of getting four?
Answer:
Expectation value = 5.8
In probability, a probability distribution used to identify with in a particular interval falling value of a probability. The probability distribution describes the range of the possible value of a random variable. The probability distribution is entirely described by the cumulative distribution function. In this article we shall discuss probability distribution coin toss example problem.
Probability Distribution Coin Toss Example Problem
Example: A coin is tossed for 65times. Find the expectation value of tail with the help of using the binomial distribution.
Solution:
Consider 65 times the coin is tossed, so n = 65
When toss a coin, we get probability of tail is p = 1/2
Probability of getting tail is represent by q
q = 1 – p [p + q = 1]
q = 1 – 1/2
q = 1/2
Expectation value:
μ = E[x] = np
= 65(1/2 )
= (65/2)
μ = E[x] = 32.5
Answer:
Expectation value = μ = E[x] = 32.5
Example 2: An unbiased die is rolling for 45 times. By using the binomial distribution find the expectation value of getting four?
Solution:
Let p be probability of getting success
Let q = 1 – p probability of getting failure
Let n be number of times the dice is thrown
An unbiased dice is rolling for 45 times, the value of n = 43
When we throe a unbiased dice, probability of getting four is p = 1/6
Probability of not getting four is represent by q
q = 1 – p
= 1 – 1/6
= 6/6– 1/6
= 6-1/6
q = 5/6
Expectation value:
μ = E(x) = np
= 45 (1/6)
= 45/6
= 7.5
μ = E(x) = 7.5
Answer:
Expectation value = μ = E[x] = 7.5
Is this topic arc length of a circle hard for you? Watch out for my coming posts.
Probability Distribution Coin Toss Practice Problem
Problem:
A coin is tossed for 42 times. Find the expectation value of tail with the help of using the binomial distribution.
Answer:
Expectation value = 21
Problem:
An unbiased die is rolling for 35 times. By using the binomial distribution find the expectation value of getting four?
Answer:
Expectation value = 5.8
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