Answer:
(-3,7)
Step-by-step explanation:
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:
y = 7.8x + 26
Step-by-step explanation:
Given the following :
Pearson's r = 0.78
Average consumption of ice cream = 5 grams per week (m) with Standard deviation (sd) = 1.5 grams
Average weight = 65 kg with standard deviation of 15kg
Formular for the regression line :
General regression formula :
y = mx + c
y = predicted variable ; m = slope or gradient ; x = predictor variable ; c = intercept
Gradient (m) = change in y / change in x
m = (sd y / sd x) * r
m = (sd weight / sd ice cream) × r
m = (15 / 1.5) × r
m = 10 × 0.78 = 7.8
Intercept:
mean of weight(y) - [Slope×mean of icecream(x)]
65 - [7.8 × 5]
65 - 39 = 26
Hence,
y = 7.8x + 26
5*0.6=3
3*0.6=1.8
1.8*0.6=1.08
5+(3*2)+(1.8*2)+(1.08*2)=16.76 ft
