Step 1: Understand the problem
We are given a binomial random variable Y, which counts the number of successes in n independent trials. The success rate for each trial is 0.3. We need to find the mean and variance of Y.

Step 2: Use the formulas for the mean and variance of a binomial distribution
The mean (μ) and variance (σ^2) of a binomial distribution are given by the formulas:

Mean (μ) = n*p
Variance (σ^2) = n*p*(1-p)

where n is the number of trials and p is the probability of success on each trial.

Step 3: Substitute the given values into the formulas
Substitute n for the number of trials and 0.3 for p in the formulas:

Mean (μ) = n*0.3
Variance (σ^2) = n*0.3*(1-0.3)

Step 4: Simplify the expressions
Mean (μ) = 0.3n
Variance (σ^2) = 0.3n*0.7 = 0.21n

So, the mean and variance of Y are 0.3n and 0.21n, respectively.

Question

Step 1: Understand the problem
We are given a binomial random variable Y, which counts the number of successes in n independent trials. The success rate for each trial is 0.3. We need to find the mean and variance of Y.

Step 2: Use the formulas for the mean and variance of a binomial distribution
The mean (μ) and variance (σ^2) of a binomial distribution are given by the formulas:

Mean (μ) = n*p
Variance (σ^2) = n*p*(1-p)

where n is the number of trials and p is the probability of success on each trial.

Step 3: Substitute the given values into the formulas
Substitute n for the number of trials and 0.3 for p in the formulas:

Mean (μ) = n*0.3
Variance (σ^2) = n*0.3*(1-0.3)

Step 4: Simplify the expressions
Mean (μ) = 0.3n
Variance (σ^2) = 0.3n*0.7 = 0.21n

So, the mean and variance of Y are 0.3n and 0.21n, respectively.

Knowee AI · Accepted Answer

Step 1: Understand the problem
We are given a binomial random variable Y, which counts the number of successes in n independent trials. The success rate for each trial is 0.3. We need to find the mean and variance of Y.

Step 2: Use the formulas for the mean and variance of a binomial distribution
The mean (μ) and variance (σ^2) of a binomial distribution are given by the formulas:

Mean (μ) = n*p
Variance (σ^2) = n*p*(1-p)

where n is the number of trials and p is the probability of success on each trial.

Step 3: Substitute the given values into the formulas
Substitute n for the number of trials and 0.3 for p in the formulas:

Mean (μ) = n*0.3
Variance (σ^2) = n*0.3*(1-0.3)

Step 4: Simplify the expressions
Mean (μ) = 0.3n
Variance (σ^2) = 0.3n*0.7 = 0.21n

So, the mean and variance of Y are 0.3n and 0.21n, respectively.

Given a Binomial random variable Y which counts the number of successes in n independent trials and the successful rate for each trial is 0.3. Find the mean and variance of Y, respectively. (The 1st number is the mean and the 2nd is the variance.)

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