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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Answer:
14n
Step-by-step explanation:
just rearrange the number with the variable
Answer:
4.5
Step-by-step explanation:
We can simplify ratios to one to find the answer
4 pounds is about 2 kilograms
2 pounds is about 1 kilogram
1 pound is about half a kilogram
9 pounds x 0.5 = 4.5
Answer:
Step-by-step explanation:
Assuming a normal distribution for the amount spent by Canadian households for high-speed broadband access, the formula for normal distribution is expressed as
z = (x - u)/s
Where
x = amount spent by the Canadian households.
u = mean amount spent monthly.
s = standard deviation
From the information given,
u = $80.63 CDN
s = $27.32 CDN
We want to find the probability that the average amount will exceed $85. It is expressed as
P(x greater than 85) = 1 - P(x lesser than or equal to 85)
For x = 85
z = (85 - 80)/27.32 = 0.18
Looking at the normal distribution table, the corresponding z score is 0.57142
P(x greater than 85) = 1 - 0.57142 = 0.43
