If XX is a binomial random variable, compute the mean, the standard deviation, and the variance for each of the following cases: (a) n=4,p=0.4n=4,p=0.4 μ=μ= σ2=σ2= σ=σ= (b) n=4,p=0.8n=4,p=0.8 μ=μ= σ2=σ2= σ=σ= (c) n=3,p=0.5n=3,p=0.5 μ=μ= σ2=σ2= σ=σ= (d) n=5,p=0.8n=5,p=0.8 μ=μ= σ2=σ2= σ=σ=

(a) The mean, variance and standard deviation of X are 1.60, 0.96 and 0.98 respectively.

(b) The mean, variance and standard deviation of X are 3.20, 0.64 and 0.80 respectively.

(c) The mean, variance and standard deviation of X are 1.50, 0.75 and 0.87 respectively.

(d) The mean, variance and standard deviation of X are 4.00, 0.80 and 0.89 respectively.

Step-by-step explanation:

The random variable X follows a Binomial distribution with parameters n and p.

The mean, variance and standard deviation of X are:

(a)

For n = 4 and p = 0.40 compute the mean, variance and standard deviation of X as follows:

Thus, the mean, variance and standard deviation of X are 1.60, 0.96 and 0.98 respectively.

(b)

For n = 4 and p = 0.80 compute the mean, variance and standard deviation of X as follows:

Thus, the mean, variance and standard deviation of X are 3.20, 0.64 and 0.80 respectively.

(c)

For n = 3 and p = 0.50 compute the mean, variance and standard deviation of X as follows:

Thus, the mean, variance and standard deviation of X are 1.50, 0.75 and 0.87 respectively.

(d)

For n = 5 and p = 0.80 compute the mean, variance and standard deviation of X as follows:

Thus, the mean, variance and standard deviation of X are 4.00, 0.80 and 0.89 respectively.

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