We will be converting X to standard normal variable Z~N(0, 1) so that we can use its cumlative distribution function (CDF) tables.
1)P(X>=6) = P(Z>= (6-6)/4) = P(Z >= 0) = 1 - P(Z < 0) = 1 - CDF(Z=0) = 0.5
2.P(3 <= X < 7) = P((3 - 6)/4 <= Z < (7 - 6)/4) = P(-0.75 <= Z < 0.25) = P(Z < 0.25) - P(Z <= -0.75)
= 0.5987 - 0.2266 = 0.3721
3.P(-1.5 <= X < 2.5) = P((-1.5 - 6)/4 <= Z < (2.5 - 6)/4) = P(-1.875 < Z < -0.875) = P(Z < -0.875) - P(Z < -1.875)
= 0.1604
4.P(-2 <= X-2 < 5) = P((-2+2)/4 <= Z < (5+2)/4) = P(0 <= Z < 1.5) = P(Z < 1.5) - P(Z < 0)
= 0.4332
If continuous random variable X~ N(6,4), compute * 1) Probability P(X>6.) 2) Probability P(3.<X<7.) 3) Probability...
If continuous random variable X~ N(6,4), compute 1) Probability P(X>6.) 2) Probability P(3.<X<7.) 3) Probability P(-1.5 <X<2.5) 4) Probability P(-2.<X – 2<5.) Show your explanations. Displaying only the final answer is not enough to get credit. Note: round calculated numerical values to the fourth decimal place where applicable.
Let descrete random variable X ~ Poisson(7). Find: 1) Probability P(X = 8) 2) Probability P(X = 3) 3) Probability P(X<4) 4) Probability P(X> 7) 5) ux 6) 0x Show your explanations. Displaying only the final answer is not enough to get credit. Note: round calculated numerical values to the fourth decimal place where applicable.
Let descrete random variable X ~ Bin(9,0.4) Find: 1) Probability P(X> 4) 2) Probability P(X> 2) 3) Probability P(2<X<5) 4) Probability P(2<X<5) 5) Probability P(X=0) 6) Probability P(X=6) 7) ux 8) TX Show your explanations. Displaying only the final answer is not enough to get credit. Note: round calculated numerical values to the fourth decimal place where applicable.
Let descrete random variable X ~ Bin(9,0.4) Find: 1) Probability P(X>4) 2) Probability P(X> 2) 3) Probability P(2 <X<5) 4) Probability P(2<X<5) 5) Probability P(X =0) 6) Probability P(X =6) 7) ux 8) OX Show your explanations. Displaying only the final answer is not enough to get credit. Note: round calculated numerical values to the fourth decimal place where applicable.
Let descrete random variable X - Bin(9,0.3) Find: 1) Probability P(X>5) 2) Probability P( X 2 ) 3) Probability P(2<x<5) 4) Probability P(2<x<5) 5) Probability P(X=0) 6) Probability P(X= 7) 7 Mx 8) Ox Show your explanations. Displaying only the final answer is not enough to get credit Note: round calculated numerical values to the fourth decimal place where applicable.
The lifetime, in years, of a certain type of pump is a random variable with probability density function x 20 (x+1) 0 True (Note: "True" means "Otherwise" or "Elsewere") 1) What is the probability that the pump lasts more than 3 years? 2) What is the probability that the pump lasts between 1 and 2 years? 3) Find the mean lifetime. 4) Find the variance of the lifetime. 5) Find the cumulative distribution function of the lifetime. 6) Find the...
x 20 The lifetime, in years, of a certain type of pump is a random variable with probability density function 3 (x+1)+ 0 True (Note: “True" means “Otherwise” or “Elsewere") 1) What is the probability that the pump lasts more than 3 years? 2) What is the probability that the pump lasts between 1 and 2 years? 3) Find the mean lifetime. 4) Find the variance of the lifetime. 5) Find the cumulative distribution function of the lifetime. 6) Find...
Please help with parts 3, 4, 5 & 6 { Elongation (in %) of steel plates treated with aluminum are random with probability density function 15 SX < 30 7875 0 True (Note: "True" means "Otherwise" or "Elsewere") 1) What proportion of steel plates have elongations greater than 25%? 2) Find the mean elongation. 3) Find the variance of the elongations. 4) Find the standard deviation of the elongations. 5) Find the cumulative distribution function of the elongations. 6) A...
{ 7875 Elongation (in %) of steel plates treated with aluminum are random with probability density function 15 sxs 30 True (Note: "True" means "Otherwise" or "Elsewere") 1) What proportion of steel plates have elongations greater than 25%? 2) Find the mean elongation. 3) Find the variance of the elongations, 4) Find the standard deviation of the elongations. 5) Find the cumulative distribution function of the elongations. 6) A particular plate elongates 20%. What proportion of plates elongate more than...
Find the area under the standard normal probability density function 1) To the right of z=-0.6 2) Between z=0.3 and z=0.9 3) Between z=-0.33 and z=0.33 4) Outside z=-1.1 to z=0.33 Show your explanations. Displaying only the final answer is not enough to get credit. Note: round calculated numerical values to the fourth decimal place where applicable.