X and Y are independent, X ~U(0,1) and Y~U(0,1). Calculate the probability P(X+Y<1.5).

Q: Let X - Unif(0, 2) and Y - Unif(0, 1). Find the probability P(X > Y) that X is greater than Y

A: # Here  given that X~U nia,b       fx =1b-a   '   a≤x≤b  0            ' other

Q: Let the joint density of the continuous random variables X ({ (1² + 2 xy) if 0 < x < 1; 0 <y<1 f(x,…

A: This is a problem of joint distribution.

Q: Determine k so thatf(x, y) = kx(x − y) for 0 &lt; x &lt; 1, −x &lt; y &lt; x0 elsewherecan serve as…

A:

Q: The random variables X and Y have joint pdf (x(1+3y²) fxy (x, y) = 0 < x < 2, 0< y < 1 4 0,…

A: Solution: The joint pdf of (X,Y) is given by  fXY(x,y)=x(1+3y2)4     0&lt;x&lt;2,  0&lt;y&lt; 10…

Q: let flx)=, V2 Cunsrder y=x? Find the probability densily funchon of Y

A:

Q: Let X be a continuous random variable symmetric about Y. Let Z = 1 if X>Y OR Z = 0 if X <= Y. Find…

A: Given: Z=1 if X&gt;Y OR Z=0 if X&lt;=Y

Q: The joint PDF of two jointly continuous random variables X and Y is c(x² + y?) for 0 < x <1 and 0 <…

A: We have given that,  X and Y two continuous random variables having joint PDF is,

Q: Find the joint probability density of the two randomvariables X and Y whose joint distribution…

A:

Q: The joint probability mass function of the random variables (X, Y) is given by the followin cable.…

A: We have given joint distribution of X and Y and we have to find the var(X+Y)

Q: Let x be a random variable with a probability density function defined by the form f(x) = ke */2, x…

A: We have given that X be a random variable with a probability density function defined by the form…

Q: The random variable X has the probability density function f(x) given by: 3 x², Ix| a) = , then a…

A: given,f(x)=3128x2      ;  x&lt;40                ;  otherwise

Q: I toss a fair coin twice, and let X be defined as the number of heads I observe. Find the range of…

A: Given that  A fair cion tossed twice  Total outcomes=22=4 Sample space=S=(HH,HT,TH,TT) X=Number of…

Q: The probability mass function of a random variable X is as follows: frx) = x! x = 0, 1, 2, ... Given…

A:

Q: (a) the joint probability function f(x, y),

A:

Q: Let X represent the number of tires with low air pressure on a randomly chosen car. a. Which of the…

A: a. Consider a random variable x with probability mass function of p(x). The necessary conditions to…

Q: Two random variables X and Y have the joint pdf, fx, y(x, y) = Ae12x+y), = 0, X, y 2 0 elséwhere (1)…

A:

Q: Let X and Y be independent random variables, prove that Var (XY) = Var (X) Var (Y) if E [X] = E [ Y]…

A: Answer: For the given data, We have,

Q: The probability density function of a random variable is kx³ f(x) = if 0 < x< 2 V25 – x2 =D0…

A: Let X be a random variable. The probability density function of X is f(x). f(x) is a probability…

Q: Let X and Y be two jointly continuous random variables with joint PDF y2 0 < x < 1,0 < y < 2 xy 4 4…

A:

Q: Let the joint pdf of random variables X, Y be fx,y (r, y) = axye-2-3y, for all æ > 0, y 2 0. Find a,…

A: We have given that a joint pdf of variables X and Y.

Q: Determine the value of k such that the function f(x y)= 4kxy for 0<x<1.5 and 0<y<1.5 satisfies the…

A:

Q: Let X and Y be continuous random variables with joint distribution function,   F (x,y).  Let g…

A:

Q: The probability density function of X random variable is given as, f(x)=c(x2 +1), -2<x<2 and f(x)=0,…

A: Given,f(x)=c(x2+1)  ;  -2≤x≤2

Q: Let fx,y (x, y) be the joint probability function for the random vector (X,Y) (discrete or…

A: fx(1) = 0 f(1,y) = 0

Q: I toss a coin 4 times, and let X be defined as the number of heads I observe. Find the range of X,…

A:

Q: The continuous joint random variables (X, Y, Z) have the joint pdf f (x, y,z) a, for 0 0. Write…

A:

Q: A random process is defined as X (t) = cos 2 t, where S2 is a uniform random variable over (0, oo)…

A:

Q: If the probability density function of a continuous random variable X is [.5x 0< x<2 f(x)= otherwise…

A:

Q: The random variables X and Y are independent and have probability masses given by: Р(X — 1) — 0.2…

A: Given, the random variables X and Y are independent. P(X=1)=0.2, P(X=2)=0.2, and P(X=3)=0.6.…

Q: A local bakery specializes in croissants and doughnuts. Let p(z, y) be the joint probability density…

A: The cost function is to be formulated for this problem, according to the problem the bakery charges…

Q: Find the exact probability density of the sum W = X + Y.

A:

Q: Var (Y) = E (Y2) - E (Y)2

A: Given that y be a continuous randomvariableThen, we know

Q: The Exponential pdf for continuous random variable Y takes the form y > 0 fV) = for B > 0. y 2+t|Y…

A:

Q: Let fxr(r, y) be the joint probability function for the random vector (X, Y) (discrete or…

A: We have given that the fX,Y(x, y) be joint distribution function for a random vector ( X, Y )[…

Q: Find the joint probability density of the two randomvariables X and Y whose joint distribution…

A:

Q: fXY (x, y) = - \xl – lyl, 00 < * < co, - 00 <y < 00 %3D (i) Are X and Y statistically independent…

A:

Q: H/W: if X and Y are continuous random variables, prove E[X] = E[E[X|Y]]? %3D

A:

Q: Let X and Y be two independent random variables, X ∼ Γ(α, λ) and Y ∼ Γ(β, λ). Find the joint…

A: It is an important fact in statistics . It is a basic instance in probability distribution theory .

Q: X and Y are two random variables (RVs) whose joint pdf is f(x,y). V and W are two RVs that are…

A: X and Y are two random variables. f (x, y)= Joint pdf (1)  Fv (v)=P (V≤v)=P (X+Y≤v)=∫y=-∞∞∫-∞V=y fxy…

Q: The joint PDF of two jointly continuous random variables X and Y is S(x2 +y?) for 0 < x < 1 and 0 <…

A: We have given that,  X and Y two continuous random variables having PDF is,

Q: Let X1 and X2 be continuous random variables with the joint probability - function fx1,x,(x1, x2),…

A: Hello! As you have posted 2 different questions, we are answering the first question (2.2.5). In…

Q: Let Y and Y, be independent and uniformly distributed over the interval (0, 1). Find the probability…

A:

Q: The joint PDF of two jointly continuous random variables X and Y is Sc(a? + y²) for 0 < x < 1 and 0…

A: From the given information, fx,y=cx2+y2, 0≤x≤1, 0≤y≤1 c=32EY=58 EY|X=32X2+143X2+1 Consider,…

Q: (a) Let Y be a random variable distributed as X. Determine E(VY) in terms of r.

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer one question at a…

Q: Show that the function f(t) = -,te Z 21 %3D 5SIS 10, defines a discrete probability distribution by…

A:

Q: Let X and Y be two continuous random variables with joint pdf f(x, y) = cx²y(1+y) for 0 ≤ x ≤ 3 and…

A: Given: Consider X and Y be two continuous random variables having cdf  f(x, y) = cx2 y(1+y)…

Q: The joint pdf of two variables X and Y is fxy(x, y) = 18 X and Y are independent random variables.…

A:

Q: Let Y be a discrete random variable.  Let c be a constant.   PROVE  Var (Y) = E (Y2) - E (Y)2

A: We have to deduce the formula of variance.

Q: Let random variables X₁ and X₂ be uncorrelated and each distributed according to fx(x) = { 0≤x≤T,…

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts.  In case…

Q: Let X be a continuous random variable with p.d.f. f(x) and distribution func Y = X², (a) what is the…

A: Given information: Let X be a continuous random variable with pdf f(x) and the distribution function…

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!