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Let X be the random variable giving the number of heads obtained in 162 successive tosses of a biased coin with probability of getting head in a toss is 1/3. Assume that the losses are in dependent. The standard deviation of X is.
- a)6
- b)8
- c)7
- d)9
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Let X be the random variable giving the number of heads obtained in 16...
Random variable x, follows Binomial distribution with n = 162, p = 1/3so, q = 1 - p = 2/3
variance = npq = 162(1/3)(2/3) = 36
⇒ standard deviation = √variance = 6
variance = npq = 162(1/3)(2/3) = 36
⇒ standard deviation = √variance = 6
Most Upvoted Answer
Let X be the random variable giving the number of heads obtained in 16...
Given:
- Random variable X represents the number of heads obtained in 162 successive tosses of a biased coin, where the probability of getting a head in a toss is 1/3.
- The tosses are assumed to be independent.
To find:
The standard deviation of X.
Solution:
Step 1: Determine the distribution of X
Since X represents the number of heads obtained in 162 tosses of a biased coin, X follows a binomial distribution with parameters n = 162 (number of trials) and p = 1/3 (probability of success - getting a head).
Step 2: Calculate the mean of X
The mean of a binomial distribution is given by the formula:
mean (μ) = n * p
Substituting the given values: μ = 162 * (1/3) = 54
Step 3: Calculate the variance of X
The variance of a binomial distribution is given by the formula:
variance (σ^2) = n * p * (1 - p)
Substituting the given values: σ^2 = 162 * (1/3) * (1 - 1/3) = 108 * (2/3) = 72
Step 4: Calculate the standard deviation of X
The standard deviation (σ) is the square root of the variance.
Taking the square root of the variance calculated in the previous step: σ = √72 = 6√2
Step 5: Simplify the standard deviation
To simplify the standard deviation, approximate the value of √2 to a decimal approximation:
√2 ≈ 1.414
Therefore, the standard deviation of X is approximately equal to 6 * 1.414 = 8.484
Answer: The correct option is A) 6.
- Random variable X represents the number of heads obtained in 162 successive tosses of a biased coin, where the probability of getting a head in a toss is 1/3.
- The tosses are assumed to be independent.
To find:
The standard deviation of X.
Solution:
Step 1: Determine the distribution of X
Since X represents the number of heads obtained in 162 tosses of a biased coin, X follows a binomial distribution with parameters n = 162 (number of trials) and p = 1/3 (probability of success - getting a head).
Step 2: Calculate the mean of X
The mean of a binomial distribution is given by the formula:
mean (μ) = n * p
Substituting the given values: μ = 162 * (1/3) = 54
Step 3: Calculate the variance of X
The variance of a binomial distribution is given by the formula:
variance (σ^2) = n * p * (1 - p)
Substituting the given values: σ^2 = 162 * (1/3) * (1 - 1/3) = 108 * (2/3) = 72
Step 4: Calculate the standard deviation of X
The standard deviation (σ) is the square root of the variance.
Taking the square root of the variance calculated in the previous step: σ = √72 = 6√2
Step 5: Simplify the standard deviation
To simplify the standard deviation, approximate the value of √2 to a decimal approximation:
√2 ≈ 1.414
Therefore, the standard deviation of X is approximately equal to 6 * 1.414 = 8.484
Answer: The correct option is A) 6.
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Community Answer
Let X be the random variable giving the number of heads obtained in 16...
Random variable x, follows Binomial distribution with n = 162, p = 1/3so, q = 1 - p = 2/3
variance = npq = 162(1/3)(2/3) = 36
⇒ standard deviation = √variance = 6
variance = npq = 162(1/3)(2/3) = 36
⇒ standard deviation = √variance = 6
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Let X be the random variable giving the number of heads obtained in 162 successive tosses of a biased coin with probability of getting head in atoss is 1/3.Assume that the losses are in dependent. The standarddeviation of X is.a)6b)8c)7d)9Correct answer is option 'A'. Can you explain this answer?
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Let X be the random variable giving the number of heads obtained in 162 successive tosses of a biased coin with probability of getting head in atoss is 1/3.Assume that the losses are in dependent. The standarddeviation of X is.a)6b)8c)7d)9Correct answer is option 'A'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about Let X be the random variable giving the number of heads obtained in 162 successive tosses of a biased coin with probability of getting head in atoss is 1/3.Assume that the losses are in dependent. The standarddeviation of X is.a)6b)8c)7d)9Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let X be the random variable giving the number of heads obtained in 162 successive tosses of a biased coin with probability of getting head in atoss is 1/3.Assume that the losses are in dependent. The standarddeviation of X is.a)6b)8c)7d)9Correct answer is option 'A'. Can you explain this answer?.
Let X be the random variable giving the number of heads obtained in 162 successive tosses of a biased coin with probability of getting head in atoss is 1/3.Assume that the losses are in dependent. The standarddeviation of X is.a)6b)8c)7d)9Correct answer is option 'A'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about Let X be the random variable giving the number of heads obtained in 162 successive tosses of a biased coin with probability of getting head in atoss is 1/3.Assume that the losses are in dependent. The standarddeviation of X is.a)6b)8c)7d)9Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let X be the random variable giving the number of heads obtained in 162 successive tosses of a biased coin with probability of getting head in atoss is 1/3.Assume that the losses are in dependent. The standarddeviation of X is.a)6b)8c)7d)9Correct answer is option 'A'. Can you explain this answer?.
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