For the given probability mass function of X, the mean is 3.5 and the standard deviation is 1.708.
- A discrete random variable X's probability mass function (PMF) is a function over its sample space that estimates the likelihood that X will have a given value. f(x)=P[X=x].
- The total of all potential values for a random variable X, weighted by their relative probabilities, is known as the mean (or expected value E[X]) of that variable.
- Mean(μ) = 1(1/6) + 2(1/6) + 3(1/6) + 4(1/6) + 5(1/6) + 6(1/6).
- Mean(μ) = (1+2+3+4+5+6)/6
- Mean(μ) = 21/6
- Mean(μ) = 3.5
- The square root of the variance of a random variable, sample, statistical population, data collection, or probability distribution represents its standard deviation. It is denoted by 'σ'.
- A random variable's variance (or Var[X]) is a measurement of the range of potential values. It is, by definition, the squared expectation of the distance between X and μ. It is denoted by 'σ²'.
- σ² = E[X²]−μ²
- σ² = [1²(1/6) + 2²(1/6) + 3²(1/6) + 4²(1/6) + 5²(1/6) + 6²(1/6)] - (3.5)²
- σ² = [(1² + 2²+ 3² + 4²+ 5²+ 6²)/6] - (3.5)²
- σ² = [(1 + 4 + 9 + 16 + 25 + 36)/6] - (3.5)²
- σ² = (91/6) - (3.5)²
- σ² = 15.167-12.25
- σ² = 2.917
- σ = √2.917
- Standard deviation (σ) = 1.708
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Over which interval(s) is the function decreasing?
Answer:
Step-by-step explanation:
is the same as 4/3 so you'd be multiplying 4/3 x 4/3 so you multiply straight across to get 16/9 when you simplify you are left with 1 7/9
Hope that helps and have a great day!
Answer:
{-7,5,18,24,32}
Step-by-step explanation:
Let's verify all cases to determine the solution to the problem.
CASE A) we have
-9,7,15,22,26
The number 22 is not included in the solution set of the compound inequality.
CASE B) we have
-7,5,18,24,32
The number 22 is not included in the solution set of the compound inequality.
CASE C) we have
16,17,22,23,24
The number 22 is not included in the solution set of the compound inequality.
CASE D) we have
18,19,20,21,22
The numbers 19,20,21,22 are not included in the solution set of the compound inequality.
Step-by-step explanation:
