A random variable

following a binomial distribution with success probability

across

trials has PMF

where

.
The mean of the distribution is given by the expected value which is defined by

where the summation is carried out over the support of

. So the mean is

Because this is a proper distribution, you have

which is a fact that will be used to evaluate the sum above.





Letting

, this becomes

Observe that the remaining sum corresponds to the PMF of a new random variable

which also follows a binomial distribution with success probability

, but this time across

trials. Therefore the sum evaluates to 1, and you're left with

as the expression for the mean for

.
Answer:
(3) Diagonals are perpendicular
Step-by-step explanation:
Answer:
Step-by-step explanation:
Since the line segment is only being translated and reflected it would still maintain its length. This is pretty much the only characteristic that would remain the same as te original line segment. It would not maintain the same x-axis positions for both endpoints of the line segment. This is because when it is translated 2 units up it is only moving on the y-axis and not the x-axis. But when it is reflected over the y-axis the endpoints flip and become the opposite values.
Answer:
I have known a man who uses math in their job/career to do problem solving. I have kind of discussed him about the dynamics of his job in terms of utilizing his math knowledge.
Step-by-step explanation:
I have known a man who uses math in their job/career. I have kind of discussed him about the dynamics of his job in terms of utilizing his math knowledge.
He mentioned that he normally does a lot of problem solving tasks on a regular basis as he likes to observe the situation logically and then solving accordingly based on critical thinking and logic.
He mentioned some of his problem solving skills using which he tends to do a lot of problem solving tasks. These problem skills are as follows:
- Understanding the logic and implementing it
- Logical calculations to solve the problem
Keywords: problem solving, communication, observation
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