हिंदी

The Probability Distribution Function of Continuous Random Variable X is Given by F( X ) = X/4, 0 < X < 2 = 0, Otherwise Find P( X ≤ 1) - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

The probability distribution function of continuous random variable X is given by
f( x ) = `x/4`,  0 < x < 2
        = 0,       Otherwise
Find P( x ≤ 1)

योग

उत्तर

P( x ≤ 1) = `int_0^1 f( x )` dx

              = `int_0^1 x/4` dx

              = `[ x^2/8 ]_0^1`

              = `1/8`

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
2015-2016 (March)

APPEARS IN

वीडियो ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्न

Examine the following function for continuity:

f (x) = x – 5


Discuss the continuity of the following functions at the indicated point(s): 

(i) \[f\left( x \right) = \begin{cases}\left| x \right| \cos\left( \frac{1}{x} \right), & x \neq 0 \\ 0 , & x = 0\end{cases}at x = 0\]

 


Discuss the continuity of the following functions at the indicated point(s): 

\[f\left( x \right) = \left\{ \begin{array}{l}\frac{1 - x^n}{1 - x}, & x \neq 1 \\ n - 1 , & x = 1\end{array}n \in N \right.at x = 1\]

Discuss the continuity of the following functions at the indicated point(s): 

\[f\left( x \right) = \binom{\left| x - a \right|\sin\left( \frac{1}{x - a} \right), for x \neq a}{0, for x = a}at x = a\] 

If   \[f\left( x \right) = \begin{cases}\frac{2^{x + 2} - 16}{4^x - 16}, \text{ if } & x \neq 2 \\ k , \text{ if }  & x = 2\end{cases}\]  is continuous at x = 2, find k.


In each of the following, find the value of the constant k so that the given function is continuous at the indicated point;  \[f\left( x \right) = \begin{cases}kx + 1, if & x \leq 5 \\ 3x - 5, if & x > 5\end{cases}\] at x = 5


Prove that  \[f\left( x \right) = \begin{cases}\frac{x - \left| x \right|}{x}, & x \neq 0 \\ 2 , & x = 0\end{cases}\] is discontinuous at x = 0

 


If the functions f(x), defined below is continuous at x = 0, find the value of k. \[f\left( x \right) = \begin{cases}\frac{1 - \cos 2x}{2 x^2}, & x < 0 \\ k , & x = 0 \\ \frac{x}{\left| x \right|} , & x > 0\end{cases}\] 

 


If  \[f\left( x \right) = \left\{ \begin{array}a x^2 + b , & 0 \leq x < 1 \\ 4 , & x = 1 \\ x + 3 , & 1 < x \leq 2\end{array}, \right.\] then the value of (ab) for which f (x) cannot be continuous at x = 1, is

 


Show that f(x) = |x − 2| is continuous but not differentiable at x = 2. 


The function f (x) = sin−1 (cos x) is


Find k, if f(x) =`log (1+3x)/(5x)` for x ≠ 0

                     = k                    for x = 0

is continuous at x = 0. 


Find the value of 'k' if the function 
f(x) = `(tan 7x)/(2x)`,                   for x ≠ 0.
      = k                                        for x = 0.
is continuous at x = 0.


Examine the continuity of the following function :
f(x) = x2 - x + 9,          for x ≤ 3
      = 4x + 3,               for x > 3 
at x = 3.


f(x) = `{{:(|x|cos  1/x",", "if"  x ≠ 0),(0",", "if"  x = 0):}` at x = 0


Show that f(x) = |x – 5| is continuous but not differentiable at x = 5.


An example of a function which is continuous everywhere but fails to be differentiable exactly at two points is ______.


If f is continuous on its domain D, then |f| is also continuous on D.


`lim_("x" -> "x" //4) ("cos x - sin x")/("x"- "x" /4)`  is equal to ____________.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×