Let the random variable x have a discrete uniform distribution on the integers 8 ≤ x ≤ 10. determine the mean, μ, and variance,
σ2, of x.
1 answer:
The discrete uniform distribution is on the interval 8 ≤ x ≤ 10.
Therefore the probability density function (shown in the figure) is
P(x) = 1/3 = 1/3 for x = 8, 9, 10
= 0 otherwse
The mean is μ = 1/3.
The variance is
σ² = Σp(x) (x- μ)²
Because x - μ = 0 for x = 8,9,10, therefore
σ² = 0
Answer:
μ = 1/3
σ² = 0
Therefore the probability density function (shown in the figure) is
P(x) = 1/3 = 1/3 for x = 8, 9, 10
= 0 otherwse
The mean is μ = 1/3.
The variance is
σ² = Σp(x) (x- μ)²
Because x - μ = 0 for x = 8,9,10, therefore
σ² = 0
Answer:
μ = 1/3
σ² = 0
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Gravity : g
Mass : m
height : h
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W = Fd ( work = force x distance )
W = P ( in case of potential energy height change)
F is the force acting on the body in case of ideal ramp , the only force acting is the weight of the body
F = mg ( not just <m> as the force is mg (Newton) gravity effect)
d is the displacement in direction of force, as we have considered the force to be the weight not it's component in direction of the ramp , the change in displacement is the change in height so
d = h
W = Fd = (F = mg) x (d = h) = mgh
W = mgh = P
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Gravity : g
Mass : m
height : h
P = mgh = 3 x 9.8 x 0.45 = 13.23 Joule
Potential energy is work , from the known formula
W = Fd ( work = force x distance )
W = P ( in case of potential energy height change)
F is the force acting on the body in case of ideal ramp , the only force acting is the weight of the body
F = mg ( not just <m> as the force is mg (Newton) gravity effect)
d is the displacement in direction of force, as we have considered the force to be the weight not it's component in direction of the ramp , the change in displacement is the change in height so
d = h
W = Fd = (F = mg) x (d = h) = mgh
W = mgh = P
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If a square-shaped pool with side lengths are 3a^5 then find the area of the pool
solution:
A = (3a^5) x (3a^5)
= 9a^5+5
= 9a^10
The area of the square-shaped pool are 9a^10 based on the given side length which is 3a^5
