Answer:
(a) The mean, variance and standard deviation of <em>X </em>are 1.60, 0.96 and 0.98 respectively.
(b) The mean, variance and standard deviation of <em>X </em>are 3.20, 0.64 and 0.80 respectively.
(c) The mean, variance and standard deviation of <em>X </em>are 1.50, 0.75 and 0.87 respectively.
(d) The mean, variance and standard deviation of <em>X </em>are 4.00, 0.80 and 0.89 respectively.
Step-by-step explanation:
The random variable <em>X</em> follows a Binomial distribution with parameters <em>n</em> and <em>p</em>.
The mean, variance and standard deviation of <em>X</em> are:
(a)
For <em>n</em> = 4 and <em>p</em> = 0.40 compute the mean, variance and standard deviation of <em>X </em>as follows:
Thus, the mean, variance and standard deviation of <em>X </em>are 1.60, 0.96 and 0.98 respectively.
(b)
For <em>n</em> = 4 and <em>p</em> = 0.80 compute the mean, variance and standard deviation of <em>X </em>as follows:
Thus, the mean, variance and standard deviation of <em>X </em>are 3.20, 0.64 and 0.80 respectively.
(c)
For <em>n</em> = 3 and <em>p</em> = 0.50 compute the mean, variance and standard deviation of <em>X </em>as follows:
Thus, the mean, variance and standard deviation of <em>X </em>are 1.50, 0.75 and 0.87 respectively.
(d)
For <em>n</em> = 5 and <em>p</em> = 0.80 compute the mean, variance and standard deviation of <em>X </em>as follows:
Thus, the mean, variance and standard deviation of <em>X </em>are 4.00, 0.80 and 0.89 respectively.