Compute the probability for a random variable X with µ=10 and σ=2. Calculate P(9 < X < 11).
Compute the probability for a random variable X with µ=10 and σ=2. Calculate P(9 < X...
Let X be a random variable with E(X) = µ and V (X) = σ 2 . Let a and b be constants (fixed numbers) and define another random variable Y = aX + b. Find the E[Y ] and V [Y ] in terms of E(X) = µ and V (X) = σ 2 . From your results, tell whether adding or subtracting a constant to the random variable changes its variance.
Assume that the random variable X is normally distributed, with mean µ = 50 and standard deviation σ = 7. Compute the probability P(X ≤ 58). Be sure to draw a normal curve with the area corresponding to the probability shaded.
If the random variable X has a mean of µ and a standard deviation σ, then the mean and standard deviation, respectively, of (X − µ)/σ are μ and σ. x¯ and s. 1 and 0. 0 and 1.
Given that X is a continuous random variable that has a uniform probability distribution, and 0 < X < 8: a. Calculate P(X < 4) (to 3 significant digits). P(X < 4)= b. Determine the mean (µ) and standard deviation (σ) of the distribution (to 3 significant digits). µ = σ =
Let X have a normal distribution with µ=10 and σ=2. Determine the probability or area in the normal curve for which P(8<X<12).
Let X have a normal distribution with µ=10 and σ=2. Determine the probability or area in the normal curve for which P(8<X<12). a)0.75 b)0.2275 c)0.05 d)0.6827
A discrete random variable X is defined by the following probability distribution X 2 7 9 10 P ( X = x ) 0.08 0.12 0.38 0.42 Find the following : μ = E ( X ) E(X^2) . E ( 2X + 3 ) E ( 4X − 8 ) σ ^2 = Var ( X ) σ = SD ( X )
X is a random variable with a lognormal distribution and that Y = ln(X) ∼ N(µ, σ2 ). Prove that µX = e ^ (µ+ (σ^2)/2 )
Suppose the random variable X follows a normal distribution with mean µ = 84 and standard deviation σ = 20. Calculate each of the following: P(X > 100) P(80 < X < 144) P(124 < X < 160) P(X < 50) P(X > X*) = .0062. What is the value of X*?
If X is a normal random variable with μ =-2 and σ = 3, and has probability density function and cumulative density function fx (z), FX (z), calculate . P(-3< X < 0) F(1/4