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Verify whether f(x) = (8/7) (1/2)^x
, x = 1,2,3 is a probability mass function. If it is,
determine the following probabilities.
(a) P(X ≤ 1)
(b)P(X > 1)
(c) P(2 < X < 6)
(d)P(X ≤ 1 or X > 1)
Test for exactness and find the complete solution of y/(x-1) dx+ {ln(2x-2)+ 1/y}dy=0
Below is an incomplete probability distribution for a random variable X.
x 1 2 3 4 5 6
f(x) 0.15 0.25 0.33 0.09
(a) If f(4) = P(X = 4) = 2P(X = 5), complete the probability distribution above.
(b)Construct a probability histogram of this distribution.
(c) Find the cumulative distribution of the random variable X.
(d)Construct a graph of the cumulative distribution.
A company has 7 applicants, three women and four men. Suppose that the 7
applicants are equally qualified and that no preference is given for choosing either
gender. Let X be the random variable described by the number of women chosen to
fill the two positions.
(a) Express the probability distribution of X as a formula in combinatorial
notation.
(b)Find P(X = 1).
(c) Find P(X ≤ 1).
$$\ce{2C_4H_{10}(g) +13O_2(g) -> 8 CO_2(g) + 10H_2O(l)}$$
$65cm^3$ of butane is burnt in $65cm^3$ of oxygen. Find the volume of carbon dioxide produced.\
I would like someone to explain this to me.
A key ring contains four office keys that are identical in appearance, but only one will
open your office door. Suppose you randomly select one key and try it. If it does not
fit, you randomly select one of the three remaining keys. If it does not fit, you
randomly select one of the last two.
(a) List the elements of the sample space S using the letters H and M for “hit” and
“miss”, respectively.
(b)To each sample point in S, assign a value x of the random variable X representing
the number of keys that you try until you find the one that opens the door.
(c) Calculate the values of P(X = x) and display them in a table.
Wood paneling can be ordered in thickness of 1/16,1/8,1/4, or3/8inch. The random variable
X is the total thickness of paneling in two orders. List the elements in the sample
space.
Specify and sketch the domain of the following function
f(x,y)= (y^2 + x^2) / √(y^2 - x^2)
Identify the following as discrete or continuous random variables.
(a) Q: Total number of points scored in a football game
(b)R: Shelf life of a particular drug
(c) S: Height of the ocean’s tide at a given location
(d)T: Thickness of a hard-bound books
(e) U: Number of aircraft near-collisions in a year
(f) V: Increase in length of life attained by a cancer patient as a result of
chemotherapy
(g) W: Tensile breaking strength (in pounds per square inch) of 1-inch diameter steel
cable
(h)X: Number of drivers killed in vehicular accidents in a certain locality
(i) Y: Number of overdue accounts in a department store at a particular time.
(j) Z: Your blood pressure
The design conditions for an air-conditioned hall is
Inside condition 24°C DBT and 60% RH
Outside condition 38°C DBT and 28°C WBT
Sensible heat gain 167040 kJ/hr
Latent heat gain 41760kJ/hr
Infiltrated air 20CMM
Coil ADP 10°C 60% of total air is recirculated and mixed with conditioned air after cooling coil.
Determine i) The condition of air before entering the hall ii) The condition of air leaving the conditioner coil iii) BPF of cooling coil iv) refrigeration load on cooling coil.
#339914 on Dec 2023