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Probability Distributions

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Probability Distribution:      Probability distribution yields the possible outcomes for any random event. It is also defined based on the underlying sample space as a set of possible outcomes of any random experiment. These settings could be a set of real numbers or a set of vectors or a set of any entities. It is a part of probability and statistics. Random experiments are defined as the result of an experiment, whose outcome cannot be predicted. Suppose, if we toss a coin, we cannot predict, what outcome it will appear either it will come as Head or as Tail. The possible result of a random experiment is called an outcome. And the set of outcomes is called a sample point. With the help of these experiments or events, we can always create a probability pattern table in terms of variables and probabilities. Random Variables :      A   random variables is a real-valued function defined on the sample space of a random experiment . In other word , the domain of a random variable is the sa
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Vectors

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  Definition    The vectors are defined as an object containing both magnitude and direction. Vector describes the movement of an object from one point to another.    Vector math   can be geometrically picturised by the directed line segment. A  vector  is defined as a mathematical structure. It has many applications in the field of physics and geometry.  We know that the location of the points on the coordinate plane can be represented using the ordered pair such as (x, y). The usage of the vector is very useful in the simplification process of three-dimensional geometry. Vector Quantity :        A quatity which needs to be described using both magnitude and direction is called a vector quantity . eg.,  displacement , velocity , force , electric field , acceleration , momentum etc.  Magnitude of a Vector The magnitude of a vector is shown by vertical lines on both the sides of the given vector “|a|”. It represents the length of the vector. Mathematically, the magnitude of a vector is
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Probability

  Definition  Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are going to happen, using it. Probability can range from 0 to 1, where 0 means the event to be an impossible one and 1 indicates a certain event. .  The probability of all the events in a sample space adds  up to 1. Formula for Probability The probability formula is defined as the possibility of an event to happen is equal to the ratio of the number of favourable outcomes and the total number of outcomes Probability of event to happen P(E) = Number of favourable outcomes/Total Number of outcomes . Types of Probability There are three major types of probabilities: Theoretical Probability Experimental Probability Axiomatic Probability Theoretical Probability It is based on the possible chances of something to happen. The theoretical probability is mainly based on the reasoning behind
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Circle

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Definition :         A circle is a set of all points in a plane which are equidistant a fixed point in the plane . A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “centre”. Every line that passes through the circle forms the line of reflection symmetry. Also, it has rotational symmetry around the centre for every angle. The circle formula in the plane is given as: (x-h) 2  + (y-k) 2  = r 2 where (x,y) are the coordinate points (h,k) is the coordinate of the centre of a circle and r is the radius of a circle. Circle Shaped Objects There are many objects we have seen in the real world that are circular in shape. Some of the examples are: Ring CD/Disc Bangles Coins Wheels Button Dartboard Hula hoop Parts of Circle Annulus - The region bounded by two concentric circles. It is basically a ring-shaped object. See the figure below. Arc –  It is basically the connected curve of a circle. Sector –  A region bou
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