Caitlyn pays $2.20 in postage to mail a CD to a friend. She uses 43-cent stamps and 6-cent stamps. How many of each stamp did Ca
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A random variable following a binomial distribution over 
trials with success probability 
has PMF
Because it's a proper probability distribution, you know that the sum of all the probabilities over the distribution's support must be 1, i.e.
The mean is given by the expected value of the distribution,
The remaining sum has a summand which is the PMF of yet another binomial distribution with
trials and the same success probability, so the sum is 1 and you're left with
You can similarly derive the variance by computing
, but I'll leave that as an exercise for you. You would find that 
, so the variance here would be
The standard deviation is just the square root of the variance, which is
Because it's a proper probability distribution, you know that the sum of all the probabilities over the distribution's support must be 1, i.e.
The mean is given by the expected value of the distribution,
The remaining sum has a summand which is the PMF of yet another binomial distribution with
You can similarly derive the variance by computing
The standard deviation is just the square root of the variance, which is
Step-by-step explanation:
This is a linear equation in slope intercept form which is
where m is the slope and b is the y intercept.
The equation
Has a slope of -1/3 so this means that the slope will be decreasing. A negative linear equation increases as we go left. and decreases as we go right. The y intercept is 2. So this means the graph must pass through (0,2) and when x=0, y must be 2.
In other words, look for a line that the y values increase as we go left and decrease we go right. Also look for a point (0,2) and make sure the graph pass through it.